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1.

図書
図書
1. Matrix analysis and applied linear algebra (: set ; [main] ; solutions manual)
Carl Meyer
出版情報: Philadelphia : Society for Industrial and Applied Mathematics (SIAM), c2000  2 v. ; 25 cm.
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目次情報: 続きを見る
Preface
Linear Equations / 1.：
Introduction / 1.1：
Gaussian Elimination and Matrices / 1.2：
Gauss-Jordan Method / 1.3：
Two-Point Boundary Value Problems / 1.4：
Making Gaussian Elimination Work / 1.5：
Ill-Conditioned Systems / 1.6：
Rectangular Systems and Echelon Forms / 2.：
Row Echelon Form and Rank / 2.1：
Reduced Row Echelon Form / 2.2：
Consistency of Linear Systems / 2.3：
Homogeneous Systems / 2.4：
Nonhomogeneous Systems / 2.5：
Electrical Circuits / 2.6：
Matrix Algebra / 3.：
From Ancient China to Arthur Cayley / 3.1：
Addition and Transposition / 3.2：
Linearity / 3.3：
Why Do It This Way / 3.4：
Matrix Multiplication / 3.5：
Properties of Matrix Multiplication / 3.6：
Matrix Inversion / 3.7：
Inverses of Sums and Sensitivity / 3.8：
Elementary Matrices and Equivalence / 3.9：
The LU Factorization / 3.10：
Vector Spaces / 4.：
Spaces and Subspaces / 4.1：
Four Fundamental Subspaces / 4.2：
Linear Independence / 4.3：
Basis and Dimension / 4.4：
More about Rank / 4.5：
Classical Least Squares / 4.6：
Linear Transformations / 4.7：
Change of Basis and Similarity / 4.8：
Invariant Subspaces / 4.9：
Norms, Inner Products, and Orthogonality / 5.：
Vector Norms / 5.1：
Matrix Norms / 5.2：
Inner-Product Spaces / 5.3：
Orthogonal Vectors / 5.4：
Gram-Schmidt Procedure / 5.5：
Unitary and Orthogonal Matrices / 5.6：
Orthogonal Reduction / 5.7：
Discrete Fourier Transform / 5.8：
Complementary Subspaces / 5.9：
Range-Nullspace Decomposition / 5.10：
Orthogonal Decomposition / 5.11：
Singular Value Decomposition / 5.12：
Orthogonal Projection / 5.13：
Why Least Squares? / 5.14：
Angles between Subspaces / 5.15：
Determinants / 6.：
Additional Properties of Determinants / 6.1：
Eigenvalues and Eigenvectors / 7.：
Elementary Properties of Eigensystems / 7.1：
Diagonalization by Similarity Transformations / 7.2：
Functions of Diagonalizable Matrices / 7.3：
Systems of Differential Equations / 7.4：
Normal Matrices / 7.5：
Positive Definite Matrices / 7.6：
Nilpotent Matrices and Jordan Structure / 7.7：
Jordan Form / 7.8：
Functions of Nondiagonalizable Matrices / 7.9：
Difference Equations, Limits, and Summability / 7.10：
Minimum Polynomials and Krylov Methods / 7.11：
Perron-Frobenius Theory / 8.：
Positive Matrices / 8.1：
Nonnegative Matrices / 8.3：
Stochastic Matrices and Markov Chains / 8.4：
Index
Preface
Linear Equations / 1.：
Introduction / 1.1：
2.

図書
図書
2. Elementary linear algebra : applications version. 8th ed
Howard Anton, Chris Rorres
出版情報: New York : John Wiley, c2000  xvi, [8], 822 p. ; 27 cm
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目次情報: 続きを見る
Systems of Linear Equations and Matrices
Note: All relevant chapters end with Supplementary Exercises.
Determinants
Vectors in 2-Space and 3-Space / 1：
Linear Equations and Matrices
Euclidean Vector Spaces
Systems of Linear Equations
General Vector Spaces
Matrices
Inner Product Spaces
Matrix Multiplication
Eigenvalues, Eigenvectors
Algebraic Properties of Matrix Operations
Linear Transformations
Special Types of Matrices and Partitioned Matrices
Additional Topics
Matrix Transformations
Complex Vector Spaces
Computer Graphics
Answers to Exercises
Correlation Coefficient (Optional)
Photo Credits
Index / 2：
Solving Linear Systems
Echelon Form of a Matrix
Elementary Matrices: Finding A-1
Equivalent Matrices
LU-Factorization (Optional)
Real Vector Spaces / 3：
Vectors in the Plane and in 3-space
Vector Spaces
Subspaces
Span and Linear Independence
Basis and Dimension
Homogeneous Systems
Coordinates and Isomorphisms
Rank of a Matrix
Standard Inner Product on R2 and R3 / 4：
Cross Product in R3 (Optional)
Gram-Schmidt Process
Orthogonal Complements
Least Squares (Optional)
Linear Transformations and Matrices / 5：
Definition and Examples
Kernel and Range of a Linear Transformation
Matrix of a Linear Transformation
Vector Space of Matrices and Vector Space of Linear Transformations (Optional)
Similarity
Inroduction to Homogeneous Coordinates (Optional)
Definition / 6：
Properties of Determinants
Cofactor Expansion
Inverse of a Matrix
Other Applications of Determinants
Determinants from a Computational Point of View
Eigenvalues and Eigenvectors / 7：
Diagonalization and Similar Matrices
Stable Age Distribution in a Population
Markov Processes (Optional)
Diagonalization of Symmetric Matrices
Spectral Decomposition and Singular Value Decomposition (Optional)
Real Quadratic Forms
Conic Sections
Quadric Surfaces
Dominant Eigenvalue and Principal Component Analysis (Optional)
Differential Equations (Optional) / 8：
Differential Equations
Dynamical Systems
MATLAB for Linear Algebra / 9：
Input and Output in MATLAB
Matrix Operations in MATLAB
Matrix Powers and Some Special Matrices
Elementary Row Operations in MATLAB
Matrix Inverses in MATLAB
Vectors in MATLAB
Applications of Linear Combinations in MATLAB
Linear Transformations in MATLAB
MATLAB Command Summary
MATLAB Exercises / 10：
Preliminaries Sets Functions / Appendix A：
Complex Numbers Complex Numbers Complex Numbers in Linear Algebra / Appendix B：
Introduction to Proofs / Appendix C：
Answers to Odd-Numbered Exercises
Systems of Linear Equations and Matrices
Note: All relevant chapters end with Supplementary Exercises.
Determinants
3.

図書
図書
3. A guide to advanced linear algebra
Steven H. Weintraub
出版情報: Washington, DC : Mathematical Association of America, c2011  xii, 251 p. ; 24 cm
シリーズ名: Mathematical Association of America guides ; no. 6
The Dolciani mathematical expositions ; no. 44
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目次情報: 続きを見る
Preface
Vector spaces and linear transformations / 1：
Coordinates / 2：
Determinants / 3：
The structure of a linear transformation I / 4：
The structure of a linear transformation II / 5：
Bilinear, sesquilinear, and quadratic forms / 6：
Real and complex inner product spaces / 7：
Matrix groups as Lie groups / 8：
Polynomials / A：
Basic properties / A.1：
Unique factorization / A.2：
Polynomials as expressions and polynomials as functions / A.3：
Modules over principal ideal domains / B：
Definitions and structure theorems / B.1：
Derivation of canonical forms / B.2：
Bibliography
Index
Preface
Vector spaces and linear transformations / 1：
Coordinates / 2：
4.

図書
図書
4. Linear associative algebras
Alexander Abian
出版情報: New York : Pergamon Press, c1971  vii, 166 p. ; 24 cm
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5.

図書
図書
5. Elementary linear algebra. 2nd ed
Stanley I. Grossman
出版情報: Belmont, Calif. : Wadsworth Pub. Co., c1984  xv, 426 p. ; 24 cm
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Systems of Linear Equations and Matrices / 1：
Determinants / 2：
Vectors in R2 and R3 / 3：
Vector Spaces / 4：
Linear Transformations / 5：
Eigenvalues, Eigenvesors, And Canonical Forms / 6：
Mathematical Induction / Appendix 1：
Complex Numbers / Appendix 2：
The Error in Numerical Computations and Computational Complexity / Appendix 3：
Gaussian Elimination with Pivoting / Appendix 4：
Using MATLAB. / Appendix 5：
Systems of Linear Equations and Matrices / 1：
Determinants / 2：
Vectors in R2 and R3 / 3：
6.

図書
図書
6. Nonnegative matrices and applicable topics in linear algebra (: E. Horwood ; : Halsted Press)
Alexander Graham
出版情報: Chichester, West Sussex, England : E. Horwood , New York, NY, USA : Halsted Press [distributor], 1987  264 p. ; 25 cm
シリーズ名: Ellis Horwood series in mathematics and its applications
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7.

図書
図書
7. The algebraic eigenvalue problem
by J.H. Wilkinson
出版情報: Oxford : Clarendon Press, 1965  xviii, 662 p. ; 25 cm
シリーズ名: Monographs on numerical analysis
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8.

図書
図書
8. Linear algebra. 2nd ed
Serge Lang
出版情報: Reading ; Mass : Addison-Wesley, 1969,c1971,1972  xi, 400 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
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9.

図書
図書
9. A second course in linear algebra
William C. Brown
出版情報: New York : Wiley, c1988  x, 264 p. ; 24 cm
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10.

図書
図書
10. Matrix theory and applications for engineers and mathematicians (: Ellis Horwood ; : Halsted Press)
Alexander Graham
出版情報: Chichester [Eng.] : E. Horwood , New York : Halsted Press, c1979  295 p. ; 23 cm
シリーズ名: Ellis Horwood series in mathematics and its applications
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11.

図書
図書
11. Linear algebra (us ; gw)
Larry Smith
出版情報: New York : Springer-Verlag, c1978  vii, 280 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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12.

図書
図書
12. Linear algebra
Serge Lang
出版情報: Reading : Addison-Wesley, 1966  x, 294 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
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13.

図書
図書
13. The geometry of spacetime : an introduction to special and general relativity
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
14.

図書
図書
14. Multivariable calculus, linear algebra, and differential equations. 2nd ed
Stanley I. Grossman
出版情報: Orlando ; Tokyo : Academic Press, c1986  xiv, 876, 92, 10 p. ; 26 cm
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15.

図書
図書
15. An introduction to wavelets through linear algebra
Michael W. Frazier
出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
Background: Complex Numbers and Linear Algebra / 1：
Real Numbers and Complex Numbers / 1.1：
Complex Series, Euler's Formula, and the Roots of Unity / 1.2：
Vector Spaces and Bases / 1.3：
Linear Transformations, Matrices, and Change of Basis / 1.4：
Diagonalization of Linear Transformations and Matrices / 1.5：
Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6：
The Discrete Fourier Transform / 2：
Basic Properties of the Discrete Fourier Transform / 2.1：
Translation-Invariant Linear Transformations / 2.2：
The Fast Fourier Transform / 2.3：
Wavelets on $bZ_N$ / 3：
Construction of Wavelets on $bZ_N$: The First Stage / 3.1：
Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2：
Examples and Applications / 3.3：
Wavelets on $bZ$ / 4：
$ ell ^2(bZ)$ / 4.1：
Complete Orthonormal Sets in Hilbert Spaces / 4.2：
$L^2([- pi , pi ))$ and Fourier Series / 4.3：
The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4：
First-Stage Wavelets on $bZ$ / 4.5：
The Iteration Step for Wavelets on $bZ$ / 4.6：
Implementation and Examples / 4.7：
Wavelets on $bR$ / 5：
$L^2(bR)$ and Approximate Identities / 5.1：
The Fourier Transform on $bR$ / 5.2：
Multiresolution Analysis and Wavelets / 5.3：
Construction of Multiresolution Analyses / 5.4：
Wavelets with Compact Support and Their Computation / 5.5：
Wavelets and Differential Equations / 6：
The Condition Number of a Matrix / 6.1：
Finite Difference Methods for Differential Equations / 6.2：
Wavelet-Galerkin Methods for Differential Equations / 6.3：
Bibliography
Index
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
16.

図書
図書
16. Linear algebra and analysis
André Lichnerowicz ; translated by Alison Johnson
出版情報: San Francisco : Holden-Day, c1967  xv, 304 p. ; 24 cm
シリーズ名: The Mathesis series
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17.

図書
図書
17. Modern aspects of linear algebra
S.K. Godunov ; [translator, Tamara Rozhkovskaya with the participation of Scientific Books (RIMIBE NSU), Novosibirsk, Russia]
出版情報: Providence, R.I. : American Mathematical Society, c1998  xvi, 303 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 175
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18.

図書
図書
18. Linear algebra
Paul C. Shields
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c1964  xii, 288 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics / Eric Reissner, consulting editor
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19.

図書
図書
19. Linear algebra for quantum theory
Per-Olov Löwdin and Quantum Theory Project, University of Florida
出版情報: New York : John Wiley & Sons, c1998  xi, 458 p. ; 25 cm
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20.

図書
図書
20. Linear algebra. 3rd ed
Larry Smith
出版情報: New York : Springer, c1998  xii, 452 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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21.

図書
図書
21. Linear algebra
Peter D. Lax
出版情報: New York : John Wiley, c1997  xiv, 250 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Fundamentals
Duality
Linear Mappings
Matrices
Determinant and Trace
Spectral Theory
Euclidean Structure
Spectral Theory of Selfadjoint Mappings
Calculus of Vector and Matrix Valued Functions
Matrix Inequalities
Kinematics and Dynamics
Convexity
The Duality Theorem
Normed Linear Spaces
Linear Mappings Between Normed Spaces
Positive Matrices
How to Solve Systems of Linear Equations
Appendices
Bibliography
Index
List of Series Titles
Fundamentals
Duality
Linear Mappings
22.

図書
図書
22. A polynomial approach to linear algebra
Paul A. Fuhrmann
出版情報: New York ; Tokyo : Springer, c1996  xiii, 360 p. ; 24 cm
シリーズ名: Universitext
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23.

図書
図書
23. A basis for linear algebra (pbk.)
Warren Brisley
出版情報: Sydney ; New York : J. Wiley & Sons Australasia, [1973]  vi, 189 p ; 25 cm
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Inspiration
Sisters in Charge
"The Child That Be Talkin'."
I Can Tell You the Exact Moment
Coming of Age
A Hard Road Up
Leap to the Top
"Mama Never Said There'd Be Days Like This."
We've Come This Far by Faith
Sister Power
Coming Full Circle: Messages to Our Sisters
Selected Bibliography
Index
Inspiration
Sisters in Charge
"The Child That Be Talkin'."
24.

図書
図書
24. Linear algebra
[by] Ross A. Beaumont
出版情報: New York : Harcourt, Brace & World, [c1965]  xi, 216 p. ; 23 cm
シリーズ名: Harbrace College mathematics series
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25.

図書
図書
25. Analytische Geometrie und lineare Algebra. 2., umgearb. und erw. Aufl
von Otto-Heinrich Keller
出版情報: Berlin : VEB Deutscher Verlag der Wissenschaften, 1963  xii, 456 p. ; 24 cm
シリーズ名: Hochschulbücher für Mathematik ; Bd. 26
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26.

図書
図書
26. Solutions manual for Lang's linear algebra
Rami Shakarchi
出版情報: New York ; Tokyo : Springer-Verlag, c1996  xi, 183 p. ; 24 cm
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Vector Spaces
Matrices
Linear Mappings
Linear Maps and Matrices
Scalar Products and Orthogonality
Determinants
Symmetric, Hermitian, and Unitary Operators
Eigenvectors and Eigenvalues
Polynomials and Matrices
Triangulation of Matrices and Linear Maps
Polynomials and Primary Decomposition
Convex Sets
Vector Spaces
Matrices
Linear Mappings
27.

図書
図書
27. Applied linear algebra
Riaz A. Usmani
出版情報: New York : M. Dekker, c1987  vi, 258 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 105
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28.

図書
図書
28. Linear algebra. 2nd ed (: us ; : gw)
Larry Smith
出版情報: New York : Springer-Verlag, c1984  vii, 362 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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29.

図書
図書
29. Elementary linear algebra. 2nd ed (est.)
A. Wayne Roberts
出版情報: Reading, Mass. : Benjamin/Cummings Pub. Co., c1985  xv, 414 p. ; 25 cm
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30.

図書
図書
30. Linear algebra (: pbk)
Serge Lang
出版情報: Reading, Mass. : Addison-Wesley, 1966  x, 294 p. ; 21 cm
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31.

図書
図書
31. Fundamentals of linear algebra
Katsumi Nomizu
出版情報: New York : McGraw-Hill, [c1966]  x, 325 p. ; 24 cm
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32.

図書
図書
32. Advanced linear algebra (: us ; : gw)
Steven Roman
出版情報: New York ; Tokyo : Springer-Verlag, c1992  xii, 363 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 135
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33.

図書
図書
33. Multivariable mathematics : linear algebra, differential equations, calculus
[by] Richard E. Williamson [and] Hale F. Trotter
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, [1974]  ix, 630 p. ; 25 cm
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目次情報:
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
34.

図書
図書
34. Geometry and combinatorics : selected works of J.J. Seidel
edited by D.G. Corneil and R. Mathon
出版情報: Boston ; Tokyo : Academic Press, c1991  xix, 410 p. ; 24 cm
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35.

図書
図書
35. Linear algebra and matrix theory
Evar D. Nering
出版情報: New York : J. Wiley, [1963]  289 p. ; 24 cm
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36.

図書
図書
36. Linear algebra through geometry. 2nd ed (: us ; : gw)
Thomas Banchoff, John Wermer
出版情報: New York ; Tokyo : Springer-Verlag, c1992  xii, 305 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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37.

図書
図書
37. Matrices and vector spaces
William C. Brown
出版情報: New York : M. Dekker, c1991  viii, 309 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 145
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38.

図書
図書
38. Linear algebra
Paul C. Shields
出版情報: Reading, Mass. : Addison-Wesley, 1965, c1964  xii, 288 p. ; 22 cm
シリーズ名: Addison-Wesley series in mathematics
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39.

図書
図書
39. Linear algebra. 3rd ed
[by] W.H. Greub
出版情報: Berlin ; New York : Springer, 1967  xiv, 434 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 97
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40.

図書
図書
40. A geometric introduction to linear algebra. 2nd ed.
Daniel Pedoe
出版情報: Bronx, N.Y. : Chelsea Pub. Co., c1976  xi, 226 p. ; 24 cm
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41.

図書
図書
41. Introduction to vector functions
[by] James A. Hummel
出版情報: Reading, Mass. : Addison-Wesley Pub. Co, [1967]  x, 372 p ; 24 cm
シリーズ名: Addison-Wesley series in mathematics / Eric Reissner, consulting editor
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42.

図書
図書
42. Calculus : with analytic geometry and linear algebra
Leopoldo V. Toralballa
出版情報: New York : Academic Press, c1967  xv, 920 p. ; 25 cm
シリーズ名: Academic Press textbooks in mathematics
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43.

図書
図書
43. Module theory : an approach to linear algebra. 2nd ed (pbk.)
T.S. Blyth
出版情報: Oxford [England] : Clarendon Press , New York : Oxford University Press, 1990  vi, 360 p. ; 24 cm
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目次情報: 続きを見る
Modules, Vector Spaces and Algebras / 1：
Submodules; Intersections and Sums / 2：
Morphisms; Exact Sequences / 3：
Quotient Modules; Basic Isomorphism Theorems / 4：
Chain Conditions; Jordan-Holder Towers / 5：
Products and Coproducts / 6：
Free Modules; Bases / 7：
Groups of Morphisms; Projective Modules / 8：
Duality; Transposition / 9：
Matrices; Linear Equations / 10：
Inner Product Spaces / 11：
Injective Modules / 12：
Simple and Semisimple Modules / 13：
The Jacobson Radical / 14：
Tensor Products; Flat Modules; Regular Rings / 15：
Tensor Products; Tensor Algebras / 16：
Exterior Algebras, Determinants / 17：
Modules Over A Principal Ideal Domain; Finitely Generated Abelian Groups / 18：
Vector Space Decomposition Theorems; Canonical Forms Under Similarity / 19：
Diagonalisation; Normal Transformations / 20：
Modules, Vector Spaces and Algebras / 1：
Submodules; Intersections and Sums / 2：
Morphisms; Exact Sequences / 3：
44.

図書
図書
44. Linear algebra. 2nd ed
Kenneth Hoffman, Ray Kunze
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1971  viii, 407 p. ; 25 cm
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目次情報: 続きを見る
Linear Equations / 1：
Vector Spaces / 2：
Linear Transformations / 3：
Polynomials / 4：
Determinants / 5：
Elementary canonical Forms / 6：
Rational and Jordan Forms / 7：
Inner Product Spaces / 8：
Operators on Inner Product Spaces / 9：
Bilinear Forms / 10：
Appendix
Linear Equations / 1：
Vector Spaces / 2：
Linear Transformations / 3：
45.

図書
図書
45. Vectors in the plane and one-variable calculus
[by] Wilfred Kaplan, Donald J. Lewis
出版情報: New York : Wiley, c1970  xiv, 640 p. ; 25 cm
シリーズ名: Calculus and linear algebra ; v. 1
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46.

図書
図書
46. Principles of linear algebra (: pbk.)
[by] J. Larrieu ; translated from the French by Marina Smith-Kok
出版情報: New York : Gordon and Breach, [1972]  273 p. ; 24 cm
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47.

図書
図書
47. Linear algebra and matrix theory. 2nd ed
[by] Evar D. Nering
出版情報: New York : Wiley, c1970  xii, 352 p. ; 23 cm
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目次情報: 続きを見る
Introduction
Vector Spaces
Linear Transformations and Matrics
Determinants, Eigenvalues, and Similarity Transformations
Linear Functionals, Bilinear Forms, Quadratic Forms
Orthogonal and Unitary Transformations, Normal Matrices
Selected Applications of Linear Algebra
Appendix
Answers to Selected Exercises
Introduction
Vector Spaces
Linear Transformations and Matrics
48.

図書
図書
48. Linear algebra with differential equations
by Sze-Tzen Hu
出版情報: Chicago : Markham Pub. Co, c1971  xiii, 374 p. ; 24 cm
シリーズ名: Markham mathematics series
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49.

図書
図書
49. A course in linear algebra
Gareth, Williams
出版情報: New York : Gordon and Breach Science, c1972  xi, 204 p ; 24 cm
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50.

図書
図書
50. Applied linear algebra
Ben Noble
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1969  xvi, 523 p. ; 25 cm
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51.

図書
図書
51. Linear algebra
[by] George D. Mostow [and] Joseph H. Sampson
出版情報: New York : McGraw-Hill, [1969]  x, 296 p ; 23 cm
シリーズ名: International series in pure and applied mathematics
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52.

図書
図書
52. Topological geometry
Ian R. Porteous
出版情報: London ; New York : Van Nostrand Reinhold, 1969  vii, 457 p. ; 24 cm
シリーズ名: The New university mathematics series
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53.

図書
図書
53. Exterior forms and their applications
Władysław Ślebodziński ; Rev. translation from the French, [translated by Abraham Goetz]
出版情報: Warszawa : [Polish Scientific Publishers], 1970  427 p.br 25 cm
シリーズ名: Monografie matematyczne ; t. 52
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54.

図書
図書
54. Linear algebra
[by] R.R. Stoll and E.T. Wong
出版情報: New York : Academic Press, [1968]  x, 326 p. ; 24 cm
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55.

図書
図書
55. Vector spaces, many-variable calculus, and differential equations (: hard ; : pbk.)
[by] Wilfred Kaplan , Donald J. Lewis
出版情報: New York : Wiley, 1971  p. 641-1197 ; 25 cm
シリーズ名: Calculus and linear algebra ; vol. 2
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56.

図書
図書
56. Finite-dimensional linear analysis : a systematic presentation in problem form
I.M. Glazman, Ju. I. Ljubič ; translated and edited by G.P. Barker G. Kuerti
出版情報: Cambridge, Mass. : MIT Press, c1974  xiv, 520 p. ; 24 cm
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57.

図書
図書
57. Matrices and linear algebra
[by] Hans Schneider [and] George Phillip Barker
出版情報: New York : Holt, Rinehart and Winston, c1968  ix, 385 p ; 24 cm
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58.

図書
図書
58. Geometric algebra
E. Artin
出版情報: New York : Interscience Publishers, c1957  x, 214 p. ; 24 cm
シリーズ名: Interscience tracts in pure and applied mathematics ; no. 3
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59.

図書
図書
59. Linear algebra
by Kenneth Hoffman and Ray Kunze
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, 1961  332 p ; 24 cm
シリーズ名: Prentice-Hall mathematics series / Albert A. Bennett, editor
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60.

図書
図書
60. Abstract linear algebra (: us ; : gw)
Morton L. Curtis ; with revisions by Paul Place
出版情報: New York : Springer-Verlag, c1990  x, 168 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Algebraic Preliminaries
Vector Spaces and Linear Maps
Matrices and Determinants
Rings and Polynomials
Inner Product Spaces
Normed Algebras
Bibliography
Index
Algebraic Preliminaries
Vector Spaces and Linear Maps
Matrices and Determinants
61.

図書
図書
61. Introduction to matrices and linear transformations
by Daniel T. Finkbeiner, II ; drawings by Evan Gillespie
出版情報: San Francisco : W.H. Freeman , Tokyo : Charles E. Tuttle, 1960  248 p.: ill. ; 22 cm
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62.

図書
図書
62. Introduction to analytic geometry and linear algebra
Arno Jaeger
出版情報: New York : Holt, Rinehart and Winston, c1960  305 p ; 24 cm
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63.

図書
図書
63. Linear analysis and differential equations
[by] Richard C. MacCamy, Victor J. Mizel
出版情報: London,[New York] : Macmillan, c1969  xiii, 561 p ; 24 cm
シリーズ名: Textbooks in applied mathematics
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64.

図書
図書
64. Advanced mathematical methods (: pbk)
Adam Ostaszewski
出版情報: Cambridge ; New York : Cambridge University Press, 1990  xiii, 545 p. ; 23 cm
シリーズ名: LSE mathematical series
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目次情報: 続きを見る
Preface
Linear Algebra / Part I：
Vector spaces (revision) / 1：
Geometry in R / 2：
Matrices / 3：
Projections / 4：
Spectral theory / 5：
The upper triangular form / 6：
The tri-diagonal form / 7：
Inverses / 8：
Convexity / 9：
The separating hyperplane theorem / 10：
Linear inequalities / 11：
Linear programming and game theory / 12：
The simplex method / 13：
Partial derivatives (revision) / 14：
Convex functions / 15：
Non-linear programming / 16：
Advanced Calculus / Part II：
The integration process
Manipulation of integrals
Multiple integrals
Differential and difference equations (revision)
Laplace transforms
Series solutions of differential equations
Calculus of variations
Solutions to Selected Exercises / Part III：
Index
Preface
Linear Algebra / Part I：
Vector spaces (revision) / 1：
65.

図書
図書
65. An introduction to linear algebra
Hans Samelson
出版情報: New York : Wiley, c1974  xi, 265 p ; 24 cm
シリーズ名: Pure and applied mathematics : a Wiley-Interscience series of monographs, and tracts
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66.

図書
図書
66. Matrices and transformations
Anthony J. Pettofrezzo
出版情報: New York : Dover Publications, [1978, c1966] , London : Constable, 1978  x, 133p ; 21cm
シリーズ名: Dover books on advanced mathematics
Teachers' mathematics reference series
所蔵情報: loading…
目次情報: 続きを見る
Matrices / 1：
Definitions and Elementary Properties / 1.1：
Matrix Multiplication / 1.2：
Diagonal Matrices / 1.3：
Special Real Matrices / 1.4：
Special Complex Matrices / 1.5：
Inverse and Systems of Matrices / 2：
Determinants / 2.1：
Inverse of a Matrix / 2.2：
Systems of Matrices / 2.3：
Rank of a Matrix / 2.4：
Systems of Linear Equations / 2.5：
Transformation of the Plane / 3：
Mappings / 3.1：
Rotations / 3.2：
Reflections, Dilations, and Magnifications / 3.3：
Other Transformations / 3.4：
Linear Homogeneous Transformations / 3.5：
Orthogonal Matrices / 3.6：
Translations / 3.7：
Rigid Motion Transformations / 3.8：
Eigenvalues and Eigenvectors / 4：
Characteristic Functions / 4.1：
A Geometric Interpretaion of Eigenvectors / 4.2：
Some Theorems / 4.3：
Diagonalization of Matrices / 4.4：
The Hamilton-Cayley Theorem / 4.5：
Quadratic Forms / 4.6：
Classification of the Conics / 4.7：
Invariants for Conics / 4.8：
Bibliography
Answers to Odd-Numbered Exercises
Index
Matrices / 1：
Definitions and Elementary Properties / 1.1：
Matrix Multiplication / 1.2：
67.

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図書
67. Linear algebra. 4th ed (: us ; : gw)
Werner Greub
出版情報: New York : Springer-Verlag, c1975  xvi, 451 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; v. 23
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68.

図書
図書
68. Linear algebra : an introductory approach. 3d ed
[by] Charles W. Curtis
出版情報: Boston : Allyn and Bacon, [1974]  ix, 337 p ; 24 cm
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69.

図書
図書
69. Linear geometry. 2nd ed (: us ; : gw)
K.W. Gruenberg, A.J. Weir
出版情報: New York : Springer-Verlag, 1977  x, 198 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 49
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70.

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図書
70. Applied linear algebra (: Halsted ; : Ellis Horwood)
by R.J. Goult
出版情報: Chichester, Eng. : Ellis Horwood , New York : Halsted Press, 1978  196 p. ; 24 cm
シリーズ名: Ellis Horwood series in mathematics and its applications
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71.

図書
図書
71. Linear algebra with linear differential equations
Franklin Lowenthal
出版情報: New York : Wiley, c1975  xi, 305 p. ; 24 cm
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72.

図書
図書
72. Linear algebra and its applications
Gilbert Strang
出版情報: New York : Academic Press, c1976  xi, 374 p. ; 24 cm
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目次情報: 続きを見る
Matrices and Gaussian Elimination / Chapter 1：
Introduction / 1.1：
The Geometry of Linear Equations / 1.2：
An Example of Gaussian Elimination / 1.3：
Matrix Notation and Matrix Multiplication / 1.4：
Triangular Factors and Row Exchanges / 1.5：
Inverses and Transposes / 1.6：
Special Matrices and Applications / 1.7：
Review Exercises: Chapter 1
Vector Spaces / Chapter 2：
Vector Spaces and Subspaces / 2.1：
Solving Ax = 0 and Ax = b / 2.2：
Linear Independence, Basis, and Dimension / 2.3：
The Four Fundamental Subspaces / 2.4：
Graphs and Networks / 2.5：
Linear Transformations / 2.6：
Review Exercises: Chapter 2
Orthogonality / Chapter 3：
Orthogonal Vectors and Subspaces / 3.1：
Cosines and Projections onto Lines / 3.2：
Projections and Least Squares / 3.3：
Orthogonal Bases and Gram-Schmidt / 3.4：
The Fast Fourier Transform / 3.5：
Review Exercises: Chapter 3
Determinants / Chapter 4：
Properties of the Determinant / 4.1：
Formulas for the Determinant / 4.3：
Applications of Determinants / 4.4：
Review Exercises: Chapter 4
Eigenvalues and Eigenvectors / Chapter 5：
Diagonalization of a Matrix / 5.1：
Difference Equations and Powers A[superscript k] / 5.3：
Differential Equations and e[superscript At] / 5.4：
Complex Matrices / 5.5：
Similarity Transformations / 5.6：
Review Exercises: Chapter 5
Positive Definite Matrices / Chapter 6：
Minima, Maxima, and Saddle Points / 6.1：
Tests for Positive Definiteness / 6.2：
Singular Value Decomposition / 6.3：
Minimum Principles / 6.4：
The Finite Element Method / 6.5：
Computations with Matrices / Chapter 7：
Matrix Norm and Condition Number / 7.1：
Computation of Eigenvalues / 7.3：
Iterative Methods for Ax = b / 7.4：
Linear Programming and Game Theory / Chapter 8：
Linear Inequalities / 8.1：
The Simplex Method / 8.2：
The Dual Problem / 8.3：
Network Models / 8.4：
Game Theory / 8.5：
Intersection, Sum, and Product of Spaces / Appendix A：
The Jordan Form / Appendix B：
Solutions to Selected Exercises
Matrix Factorizations
Matrices and Gaussian Elimination / Chapter 1：
Introduction / 1.1：
The Geometry of Linear Equations / 1.2：
73.

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図書
73. Linear algebra and analysis
M. Zamansky
出版情報: London : D. Van Nostrand, c1969  xii, 466 p. ; 24 cm
シリーズ名: The New university mathematics series
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74.

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図書
74. Abstract and linear algebra
David M. Burton
出版情報: Reading, Mass. : Addison-Wesley, c1972  vi, 538 p. ; 25 cm
シリーズ名: Addison-Wesley series in mathematics / Eric Reissner, consulting editor
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75.

図書
図書
75. Linear algebra
Ichiro Satake ; translated by Sebastian Koh, Tadatoshi Akiba, Shin-ichiro Ihara
出版情報: New York : M. Dekker, c1975  xi, 375 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 29
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76.

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図書
76. Foundations of global non-linear analysis
Richard S. Palais
出版情報: New York : W.A. Benjamin, 1968  vii, 131 p. ; 28 cm
シリーズ名: Mathematics lecture note series
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77.

図書
図書
77. Linear algebra and geometry
Jean Dieudonné
出版情報: Paris : Hermann, c1969  207 p. ; 23 cm
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78.

図書
図書
78. Constructive linear algebra
[by] Allan Gewirtz, Harry Sitomer [and] Albert W. Tucker
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, [1974]  xi, 493 p ; 23 cm
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79.

図書
図書
79. Linear algebra and geometry (pbk.)
David M. Bloom
出版情報: Cambridge : Cambridge University Press, 1979  xiii, 625 p. ; 23 cm
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80.

図書
図書
80. A geometric introduction to linear algebra
Daniel Pedoe
出版情報: New York : Wiley, [1963]  xi, 224 p ; 24 cm
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81.

図書
図書
81. Linear algebra : an introduction
[by] Paul J. Knopp
出版情報: Santa Barbara, Calif. : Hamilton Pub. Co, 1974  xvi, 435 p ; 23 cm
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82.

図書
図書
82. Introduction to matrix theory and linear algebra
Irving Reiner
出版情報: New York : Holt, Rinehart and Winston, c1971  v, 154 p ; 23 cm
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83.

図書
図書
83. Applications of linear algebra
by Chris Rorres, Howard Anton
出版情報: New York : Wiley, c1977  ix, 233 p. ; 23 cm
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84.

図書
図書
84. Linear algebra. 2nd ed
by W.H. Greub
出版情報: Berlin : Springer, 1963  x, 338 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 97
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85.

図書
図書
85. Problems and theorems in linear algebra
V.V. Prasolov ; [translated by D.A. Leites from an original Russian manuscript ; translation edited by Simeon Ivanov]
出版情報: Providence, R.I. : American Mathematical Society, c1994  xviii, 225 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 134
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目次情報: 続きを見る
Main notations and conventions
Determinants Linear spaces
Canonical forms of matrices and linear operators
Matrices of special form Multilinear algebra
Matrix inequalities
Matrices in algebra and calculus
Appendix
Bibliography
Subject Index
Main notations and conventions
Determinants Linear spaces
Canonical forms of matrices and linear operators
86.

図書
図書
86. Linear transformations and matrices. Preliminary edition
[by] F. A. Ficken
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1964  1v. ; 22 cm
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87.

図書
図書
87. Elementary linear algebra. 2d ed
Howard Anton
出版情報: New York : Wiley, c1977  xv,366 p. in various pagings ; 24 cm
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目次情報: 続きを見る
Systems of Linear Equations and Matrices
Note: All relevant chapters end with Supplementary Exercises.
Determinants
Vectors in 2-Space and 3-Space / 1：
Linear Equations and Matrices
Euclidean Vector Spaces
Systems of Linear Equations
General Vector Spaces
Matrices
Inner Product Spaces
Matrix Multiplication
Eigenvalues, Eigenvectors
Algebraic Properties of Matrix Operations
Linear Transformations
Special Types of Matrices and Partitioned Matrices
Additional Topics
Matrix Transformations
Complex Vector Spaces
Computer Graphics
Answers to Exercises
Correlation Coefficient (Optional)
Photo Credits
Index / 2：
Solving Linear Systems
Echelon Form of a Matrix
Elementary Matrices: Finding A-1
Equivalent Matrices
LU-Factorization (Optional)
Real Vector Spaces / 3：
Vectors in the Plane and in 3-space
Vector Spaces
Subspaces
Span and Linear Independence
Basis and Dimension
Homogeneous Systems
Coordinates and Isomorphisms
Rank of a Matrix
Standard Inner Product on R2 and R3 / 4：
Cross Product in R3 (Optional)
Gram-Schmidt Process
Orthogonal Complements
Least Squares (Optional)
Linear Transformations and Matrices / 5：
Definition and Examples
Kernel and Range of a Linear Transformation
Matrix of a Linear Transformation
Vector Space of Matrices and Vector Space of Linear Transformations (Optional)
Similarity
Inroduction to Homogeneous Coordinates (Optional)
Definition / 6：
Properties of Determinants
Cofactor Expansion
Inverse of a Matrix
Other Applications of Determinants
Determinants from a Computational Point of View
Eigenvalues and Eigenvectors / 7：
Diagonalization and Similar Matrices
Stable Age Distribution in a Population
Markov Processes (Optional)
Diagonalization of Symmetric Matrices
Spectral Decomposition and Singular Value Decomposition (Optional)
Real Quadratic Forms
Conic Sections
Quadric Surfaces
Dominant Eigenvalue and Principal Component Analysis (Optional)
Differential Equations (Optional) / 8：
Differential Equations
Dynamical Systems
MATLAB for Linear Algebra / 9：
Input and Output in MATLAB
Matrix Operations in MATLAB
Matrix Powers and Some Special Matrices
Elementary Row Operations in MATLAB
Matrix Inverses in MATLAB
Vectors in MATLAB
Applications of Linear Combinations in MATLAB
Linear Transformations in MATLAB
MATLAB Command Summary
MATLAB Exercises / 10：
Preliminaries Sets Functions / Appendix A：
Complex Numbers Complex Numbers Complex Numbers in Linear Algebra / Appendix B：
Introduction to Proofs / Appendix C：
Answers to Odd-Numbered Exercises
Systems of Linear Equations and Matrices
Note: All relevant chapters end with Supplementary Exercises.
Determinants
88.

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図書
88. Principes d'algèbre linéaire
par J. Larrieu
出版情報: Paris : Dunod, 1965  168, [1] p ; 24 cm
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89.

図書
図書
89. Differential equations, dynamical systems, and an introduction to chaos. 2nd ed
Morris W. Hirsch, Stephen Smale, Robert L. Devaney
出版情報: San Diego ; Tokyo : Elsevier Academic Press, c2004  xiv, 417 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 60
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目次情報: 続きを見る
Preface
First-Order Equations / Chapter 1：
The Simplest Example / 1.1：
The Logistic Population Model / 1.2：
Constant Harvesting and Bifurcations / 1.3：
Periodic Harvesting and Periodic Solutions / 1.4：
Computing the Poincare Map / 1.5：
Exploration: A Two-Parameter Family / 1.6：
Planar Linear Systems / Chapter 2：
Second-Order Differential Equations / 2.1：
Planar Systems / 2.2：
Preliminaries from Algebra / 2.3：
Eigenvalues and Eigenvectors / 2.4：
Solving Linear Systems / 2.6：
The Linearity Principle / 2.7：
Phase Portraits for Planar Systems / Chapter 3：
Real Distinct Eigenvalues / 3.1：
Complex Eigenvalues / 3.2：
Repeated Eigenvalues / 3.3：
Changing Coordinates / 3.4：
Classification of Planar Systems / Chapter 4：
The Trace-Determinant Plane / 4.1：
Dynamical Classification / 4.2：
Exploration: A 3D Parameter Space / 4.3：
Higher Dimensional Linear Algebra / Chapter 5：
Preliminaries from Linear Algebra / 5.1：
Bases and Subspaces / 5.2：
Genericity / 5.5：
Higher Dimensional Linear Systems / Chapter 6：
Distinct Eigenvalues / 6.1：
Harmonic Oscillators / 6.2：
The Exponential of a Matrix / 6.3：
Nonautonomous Linear Systems / 6.5：
Nonlinear Systems / Chapter 7：
Dynamical Systems / 7.1：
The Existence and Uniqueness Theorem / 7.2：
Continuous Dependence of Solutions / 7.3：
The Variational Equation / 7.4：
Exploration: Numerical Methods / 7.5：
Equilibria in Nonlinear Systems / Chapter 8：
Some Illustrative Examples / 8.1：
Nonlinear Sinks and Sources / 8.2：
Saddles / 8.3：
Stability / 8.4：
Bifurcations / 8.5：
Exploration: Complex Vector Fields / 8.6：
Global Nonlinear Techniques / Chapter 9：
Nullclines / 9.1：
Stability of Equilibria / 9.2：
Gradient Systems / 9.3：
Hamiltonian Systems / 9.4：
Exploration: The Pendulum with Constant Forcing / 9.5：
Closed Orbits and Limit Sets / Chapter 10：
Limit Sets / 10.1：
Local Sections and Flow Boxes / 10.2：
The Poincare Map / 10.3：
Monotone Sequences in Planar Dynamical Systems / 10.4：
The Poincare-Bendixson Theorem / 10.5：
Applications of Poincare-Bendixson / 10.6：
Exploration: Chemical Reactions That Oscillate / 10.7：
Applications in Biology / Chapter 11：
Infectious Diseases / 11.1：
Predator/Prey Systems / 11.2：
Competitive Species / 11.3：
Exploration: Competition and Harvesting / 11.4：
Applications in Circuit Theory / Chapter 12：
An RLC Circuit / 12.1：
The Lienard Equation / 12.2：
The van der Pol Equation / 12.3：
A Hopf Bifurcation / 12.4：
Exploration: Neurodynamics / 12.5：
Applications in Mechanics / Chapter 13：
Newton's Second Law / 13.1：
Conservative Systems / 13.2：
Central Force Fields / 13.3：
The Newtonian Central Force System / 13.4：
Kepler's First Law / 13.5：
The Two-Body Problem / 13.6：
Blowing Up the Singularity / 13.7：
Exploration: Other Central Force Problems / 13.8：
Exploration: Classical Limits of Quantum Mechanical Systems / 13.9：
The Lorenz System / Chapter 14：
Introduction to the Lorenz System / 14.1：
Elementary Properties of the Lorenz System / 14.2：
The Lorenz Attractor / 14.3：
A Model for the Lorenz Attractor / 14.4：
The Chaotic Attractor / 14.5：
Exploration: The Rossler Attractor / 14.6：
Discrete Dynamical Systems / Chapter 15：
Introduction to Discrete Dynamical Systems / 15.1：
The Discrete Logistic Model / 15.2：
Chaos / 15.4：
Symbolic Dynamics / 15.5：
The Shift Map / 15.6：
The Cantor Middle-Thirds Set / 15.7：
Exploration: Cubic Chaos / 15.8：
Exploration: The Orbit Diagram / 15.9：
Homoclinic Phenomena / Chapter 16：
The Shil'nikov System / 16.1：
The Horseshoe Map / 16.2：
The Double Scroll Attractor / 16.3：
Homoclinic Bifurcations / 16.4：
Exploration: The Chua Circuit / 16.5：
Existence and Uniqueness Revisited / Chapter 17：
Proof of Existence and Uniqueness / 17.1：
Continuous Dependence on Initial Conditions / 17.3：
Extending Solutions / 17.4：
Nonautonomous Systems / 17.5：
Differentiability of the Flow / 17.6：
Bibliography
Index
Preface
First-Order Equations / Chapter 1：
The Simplest Example / 1.1：
90.

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図書
90. Linear algebra and its applications. 2nd ed, update (: International ed.)
David C. Lay
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c2000  xx, 486, 57, 12 p. ; 24 cm
シリーズ名: Addison-Wesley world student series
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目次情報: 続きを見る
Linear Equations in Linear Algebra / 1：
Introductory Example: Linear Models in Economics and Engineering
Systems of Linear Equations / 1.1：
Row Reduction and Echelon Forms / 1.2：
Vector Equations / 1.3：
The Matrix Equation Ax = b / 1.4：
Solution Sets of Linear Systems / 1.5：
Applications of Linear Systems / 1.6：
Linear Independence / 1.7：
Introduction to Linear Transformations / 1.8：
The Matrix of a Linear Transformation / 1.9：
Linear Models in Business, Science, and Engineering / 1.10：
Supplementary Exercises
Matrix Algebra / 2：
Introductory Example: Computer Models in Aircraft Design
Matrix Operations / 2.1：
The Inverse of a Matrix / 2.2：
Characterizations of Invertible Matrices / 2.3：
Partitioned Matrices / 2.4：
Matrix Factorizations / 2.5：
The Leontief Input=Output Model / 2.6：
Applications to Computer Graphics / 2.7：
Subspaces of Rn / 2.8：
Dimension and Rank / 2.9：
Determinants / 3：
Introductory Example: Determinants in Analytic Geometry
Introduction to Determinants / 3.1：
Properties of Determinants / 3.2：
Cramer's Rule, Volume, and Linear Transformations / 3.3：
Vector Spaces / 4：
Introductory Example: Space Flight and Control Systems
Vector Spaces and Subspaces / 4.1：
Null Spaces, Column Spaces, and Linear Transformations / 4.2：
Linearly Independent Sets Bases / 4.3：
Coordinate Systems / 4.4：
The Dimension of a Vector Space / 4.5：
Rank / 4.6：
Change of Basis / 4.7：
Applications to Difference Equations / 4.8：
Applications to Markov Chains / 4.9：
Eigenvalues and Eigenvectors / 5：
Introductory Example: Dynamical Systems and Spotted Owls
Eigenvectors and Eigenvalues / 5.1：
The Characteristic Equation / 5.2：
Diagonalization / 5.3：
Eigenvectors and Linear Transformations / 5.4：
Complex Eigenvalues / 5.5：
Discrete Dynamical Systems / 5.6：
Applications to Differential Equations / 5.7：
Iterative Estimates for Eigenvalues / 5.8：
Orthogonality and Least Squares / 6：
Introductory Example: Readjusting the North American Datum
Inner Product, Length, and Orthogonality / 6.1：
Orthogonal Sets / 6.2：
Orthogonal Projections / 6.3：
The Gram-Schmidt Process / 6.4：
Least-Squares Problems / 6.5：
Applications to Linear Models / 6.6：
Inner Product Spaces / 6.7：
Applications of Inner Product Spaces / 6.8：
Symmetric Matrices and Quadratic Forms / Chapter 7：
Introductory Example: Multichannel Image Processing
Diagonalization of Symmetric Matrices / 7.1：
Quadratic Forms / 7.2：
Constrained Optimization / 7.3：
The Singular Value Decomposition / 7.4：
Applications to Image Processing and Statistics / 7.5：
Supplementary Exercises (ONLINE ONLY)
The Geometry of Vector Spaces / 8：
Introductory Example: The Platonic Solids
Affine Combinations / 8.1：
Affine Independence / 8.2：
Convex Combinations / 8.3：
Hyperplanes / 8.4：
Polytopes / 8.5：
Curves and Surfaces / 8.6：
Optimization / 9：
Introductory Example: The Berlin Airlift
Matrix Games / 9.1：
Linear Programming - Geometric Method / 9.2：
Linear Programming - Simplex Method / 9.3：
Duality / 9.4：
Appendices
Uniqueness of the Reduced Echelon Form / A：
Complex Numbers / B：
Glossary
Answers to Odd-Numbered Exercises
Index
Linear Equations in Linear Algebra / 1：
Introductory Example: Linear Models in Economics and Engineering
Systems of Linear Equations / 1.1：
91.

図書
図書
91. Linear algebra with applications
Hugh G. Campbell
出版情報: New York : Appleton-Century-Crofts, c1971  xiii, 336, A39 p. ; 24 cm
シリーズ名: The Appleton-Century mathematics series
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92.

図書
図書
92. Differential equations & linear algebra. International ed.
C. Henry Edwards, David E. Penney
出版情報: Upper Saddle River, N.J. : Prentice Hall International, c2001  xiii, 684, 48, 6 p. ; 24 cm.
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目次情報: 続きを見る
First-Order Differential Equations / 1：
Differential Equations and Mathematical Model
Integrals as General and Particular Solutions
Direction Fields and Solution Curves
Separable Equations and Applications
Linear First-Order Equations
Substitution Methods and Exact Equations
Mathematical Models and Numerical Methods / 2：
Population Models
Equilibrium Solutions and Stability
Acceleration-Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Runge-Kutta Method
Linear Systems and Matrices / 3：
Introduction to Linear Systems
Matrices and Gaussian Elimination
Reduced Row-Echelon Matrices
Matrix Operations
Inverses of Matrices
Determinants
Linear Equations and Curve Fitting
Vector Spaces / 4：
The Vector Space R
The Vector Space Rn and Subspaces
Linear Combinations and Independence of Vectors
Bases and Dimension for Vector Spaces
General Vector Spaces
Linear Equations of Higher Order / 5：
Introduction: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Undetermined Coefficients and Variation of Parameters
Forced Oscillations and Resonance
Eigenvalues and Eigenvectors / 6：
Introduction to Eigenvalues
Diagonalization of Matrices
Applications Involving Powers of Matrices
Linear Systems of Differential Equations / 7：
First-Order Systems and Applications
Matrices and Linear Systems
The Eigenvalue Method for Linear Systems
Second-Order Systems and Mechanical Applications
Multiple Eigenvalue Solutions
Numerical Methods for Systems
Matrix Exponential Methods / 8：
Matrix Exponentials and Linear Systems
Nonhomogeneous Linear Systems
Spectral Decomposition Methods
Nonlinear Systems and Phenomena / 9：
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Laplace Transform Methods / 10：
Laplace Transforms and Inverse Transforms
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals, and Products of Transforms
Periodic and Piecewise Continuous Forcing Functions
Power Series Methods / 11：
Introduction and Review of Power Series
Power Series Solutions
Frobenius Series Solutions
Bessel's Equation
References for Further Study
The Existence and Uniqueness of Solutions / Appendix A：
Theory of Determinants / Appendix B：
Answers to Selected Problems
Index
First-Order Differential Equations / 1：
Differential Equations and Mathematical Model
Integrals as General and Particular Solutions
93.

図書
図書
93. Einführung in die analytische Geometrie und lineare Algebra
von Siegfried Brehmer und Horst Belkner. Mit 146 Abbildungen
出版情報: Berlin : Deutscher Verlag der Wissenschaften, 1966  xi, 364 p ; 24 cm
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94.

図書
図書
94. A (terse) introduction to linear algebra
Yitzhak Katznelson, Yonatan R. Katznelson
出版情報: Providence, R.I. : American Mathematical Society, c2008  x, 215 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 44
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Vector spaces
Linear operators and matrices
Duality of vector spaces
Determinants Invariant subspaces
Operators on inner-product spaces
Structure theorems
Additional topics
Appendix
Index
Vector spaces
Linear operators and matrices
Duality of vector spaces
95.

図書
図書
95. Linear programming with MATLAB
Michael C. Ferris, Olvi L. Mangasarian, Stephen J. Wright
出版情報: Philadelphia : Society for Industrial and Applied Mathematics : Mathematical Programming Society, c2007  xi, 266 p. ; 26 cm
シリーズ名: MPS-SIAM series on optimization ; 7
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96.

図書
図書
96. Linear and projective representations of symmetric groups (: hbk)
Alexander Kleshchev
出版情報: Cambridge : Cambridge University Press, c2005  xiv, 277 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 163
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目次情報: 続きを見る
Preface
Linear Representations / Part I：
Notations and generalities / 1：
Symmetric groups I / 2：
Degenerate affine Hecke algebra / 3：
First results on Hn-modules / 4：
Crystal operators / 5：
Character calculations / 6：
Integral representations and cyclotomic Hecke algebras / 7：
Functors ei? and fi? / 8：
Construction of UZ+ and irreducible modules / 9：
Identification of the crystal / 10：
Symmetric groups II / 11：
Projective Representations / Part II：
Generalities on superalgebra / 12：
Sergeev superalgebras / 13：
Affine Sergeev superalgebras / 14：
Integral representations and cyclotomic Sergeev algebras / 15：
First results on Xn-modules / 16：
Crystal operators for Xn / 17：
Character calculations for Xn / 18：
Operators ei? and fi? / 19：
Double covers / 20：
References
Index
Preface
Linear Representations / Part I：
Notations and generalities / 1：
97.

図書
図書
97. Geršgorin and his circles
Richard S. Varga
出版情報: Berlin : Springer, c2004  x, 226 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 36
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目次情報: 続きを見る
Preface / I：
Basic Theory / 1：
Geršgorin's Theorem / 1.1：
Extensions of Geršgorin's Theorem via Graph Theory / 1.2：
Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3：
A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4：
Geršgorin-Type Eigenvalue Inclusion Theorems / 2：
Brauer's Ovals of Cassini / 2.1：
Higher-Order Lemniscates / 2.2：
Comparison of the Brauer Sets and the Brualdi Sets / 2.3：
The Sharpness of Brualdi Lemniscate Sets / 2.4：
An Example / 2.5：
More Eigenvalue Inclusion Results / 3：
The Parodi-Schneider Eigenvalue Inclusion Sets / 3.1：
The Field of Values of a Matrix / 3.2：
Newer Eigenvalue Inclusion Sets / 3.3：
The Pupkov-Solov'ev Eigenvalue Inclusions Set / 3.4：
Minimal Geršgorin Sets and Their Sharpness / 4：
Minimal Geršgorin Sets / 4.1：
Minimal Geršgorin Sets via Permutations / 4.2：
A Comparison of Minimal Geršgorin Sets and Brualdi Sets / 4.3：
G-Functions / 5：
The Sets <$>{\cal F}_{\bf n}<$> and <$>{\cal G}_{\bf n}<$> / 5.1：
Structural Properties of <$>{\cal G}_{\bf n}<$> and <$>{\cal G}_{\bf n}^{\bf c}<$> / 5.2：
Minimal G-Functions / 5.3：
Minimal G-Functions with Small Domains of Dependence / 5.4：
Connections with Brauer Sets and Generalized Brualdi Sets / 5.5：
Geršgorin-Type Theorems for Partitioned Matrices / 6：
Partitioned Matrices and Block Diagonal Dominance / 6.1：
A Different Norm Approach / 6.2：
A Variation on a Theme by Brualdi / 6.3：
G-Functions in the Partitioned Case / 6.4：
Geršgorin's Paper from 1931, and Comments / Appendix A：
Vector Norms and Induced Operator Norms / Appendix B：
The Perron-Frobenius Theory of Nonnegative Matrices / Appendix C：
Matlab 6 Programs / Appendix D：
References
Preface / I：
Basic Theory / 1：
Geršgorin's Theorem / 1.1：
98.

図書
図書
98. Newton methods for nonlinear problems : affine invariance and adaptive algorithms
Peter Deuflhard
出版情報: Berlin ; Tokyo : Springer, c2004  xii, 424 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 35
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目次情報: 続きを見る
Outline of Contents
Introduction / 1：
Newton-Raphson Method for Scalar Equations / 1.1：
Newton's Method for General Nonlinear Problems / 1.2：
Classical convergence theorems revisited / 1.2.1：
Affine invariance and Lipschitz conditions / 1.2.2：
The algorithmic paradigm / 1.2.3：
A Roadmap of Newton-type Methods / 1.3：
Adaptive Inner Solvers for Inexact Newton Methods / 1.4：
Residual norm minimization: GMRES / 1.4.1：
Energy norm minimization: PCG / 1.4.2：
Error norm minimization: CGNE / 1.4.3：
Error norm reduction: GBIT / 1.4.4：
Linear multigrid methods / 1.4.5：
Exercises
Algebraic Equations / Part I：
Systems of Equations: Local Newton Methods / 2：
Error Oriented Algorithms / 2.1：
Ordinary Newton method / 2.1.1：
Simplified Newton method / 2.1.2：
Newton-like methods / 2.1.3：
Broyden's 'good' rank-1 updates / 2.1.4：
Inexact Newton-ERR methods / 2.1.5：
Residual Based Algorithms / 2.2：
Broyden's 'bad' rank-1 updates / 2.2.1：
Inexact Newton-RES method / 2.2.4：
Convex Optimization / 2.3：
Inexact Newton-PCG method / 2.3.1：
Systems of Equations: Global Newton Methods / 3：
Globalization Concepts / 3.1：
Componentwise convex mappings / 3.1.1：
Steepest descent methods / 3.1.2：
Trust region concepts / 3.1.3：
Newton path / 3.1.4：
Residual Based Descent / 3.2：
Affine contravariant convergence analysis / 3.2.1：
Adaptive trust region strategies / 3.2.2：
Error Oriented Descent / 3.2.3：
General level functions / 3.3.1：
Natural level function / 3.3.2：
Convex Functional Descent / 3.3.3：
Affine conjugate convergence analysis / 3.4.1：
Least Squares Problems: Gauss-Newton Methods / 3.4.2：
Linear Least Squares Problems / 4.1：
Unconstrained problems / 4.1.1：
Equality constrained problems / 4.1.2：
Local Gauss-Newton methods / 4.2：
Global Gauss-Newton methods / 4.2.2：
Adaptive trust region strategy / 4.2.3：
Local convergence results / 4.3：
Local Gauss-Newton algorithms / 4.3.2：
Global convergence results / 4.3.3：
Adaptive rank strategies / 4.3.4：
Underdetermined Systems of Equations / 4.4：
Local quasi-Gauss-Newton method / 4.4.1：
Global Gauss-Newton method / 4.4.2：
Parameter Dependent Systems: Continuation Methods / 5：
Newton Continuation Methods / 5.1：
Classification of continuation methods / 5.1.1：
Affine covariant feasible stepsizes / 5.1.2：
Adaptive pathfollowing algorithms / 5.1.3：
Gauss-Newton Continuation Method / 5.2：
Discrete tangent continuation beyond turning points / 5.2.1：
Adaptive stepsize control / 5.2.2：
Computation of Simple Bifurcations / 5.3：
Augmented systems for critical points / 5.3.1：
Newton-like algorithm for simple bifurcations / 5.3.2：
Branching-off algorithm / 5.3.3：
Differential Equations / Part II：
Stiff ODE Initial Value Problems / 6：
Affine Similar Linear Contractivity / 6.1：
Nonstiff versus Stiff Initial Value Problems / 6.2：
Picard iteration versus Newton iteration / 6.2.1：
Newton-type uniqueness theorems / 6.2.2：
Uniqueness Theorems for Implicit One-step Methods / 6.3：
Pseudo-transient Continuation for Steady State Problems / 6.4：
Exact pseudo-transient continuation / 6.4.1：
Inexact pseudo-transient continuation / 6.4.2：
ODE Boundary Value Problems / 7：
Multiple Shooting for Timelike BVPs / 7.1：
Cyclic linear systems / 7.1.1：
Realization of Newton methods / 7.1.2：
Realization of continuation methods / 7.1.3：
Parameter Identification in ODEs / 7.2：
Periodic Orbit Computation / 7.3：
Single orbit computation / 7.3.1：
Orbit continuation methods / 7.3.2：
Fourier collocation method / 7.3.3：
Polynomial Collocation for Spacelike BVPs / 7.4：
Discrete versus continuous solutions / 7.4.1：
Quasilinearization as inexact Newton method / 7.4.2：
PDE Boundary Value Problems / 8：
Asymptotic Mesh Independence / 8.1：
Global Discrete Newton Methods / 8.2：
General PDEs / 8.2.1：
Elliptic PDEs / 8.2.2：
Inexact Newton Multilevel FEM for Elliptic PDEs / 8.3：
Local Newton-Galerkin methods / 8.3.1：
Global Newton-Galerkin methods / 8.3.2：
References
Software
Index
Outline of Contents
Introduction / 1：
Newton-Raphson Method for Scalar Equations / 1.1：
99.

図書
図書
99. Linear algebra in action. 2nd ed
Harry Dym
出版情報: Providence, R.I. : American Mathematical Society, c2013  xix, 585 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 78
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100.

図書
図書
100. Dynamical systems and linear algebra
Fritz Colonius, Wolfgang Kliemann
出版情報: Providence, R.I. : American Mathematical Society, c2014  xv, 284 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 158
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