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1.

図書

図書
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:
2.

図書

図書
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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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:
3.

図書

図書
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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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
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
5.

図書

図書
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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6.

図書

図書
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
7.

図書

図書
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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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
8.

図書

図書
Carl Meyer
出版情報: Philadelphia : Society for Industrial and Applied Mathematics (SIAM), c2000  2 v. ; 25 cm.
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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:
9.

図書

図書
Morris W. Hirsch and Stephen Smale
出版情報: New York : Academic Press, c1974  xi, 358 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; v. 60
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Preface
First Examples
Newton's Equation and Kepler's Law
Linear Systems with Constant Coeffecients and Real Eigenvalues
Linear Systems with Constant Coefficients and Complex Eigenvalues
Linear Systems and Exponentials of Operators
Linear Systems and Canonical Forms of Operators
Contractions and Generic Properties of Operators
Fundamental Theory
Stability of Equilibria
Differential Equations for Electrical Circuits
The Poincare-Bendixson Theorem
Ecology
Periodic Attractors
Classical Mechanics
Nonautonomous Equations and Differentiability of Flows
Perturbation Theory and Structural Stability
Elementary Facts
Polynomials
On Canonical Forms
The Inverse Function Theorem
References
Answers to Selected Problems
Index
Preface
First Examples
Newton's Equation and Kepler's Law
10.

図書

図書
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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