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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
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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3.

図書

図書
И.М. Гразман, Ю.И. Любич
出版情報: Москва : "Наука", 1969  475 p ; 21 cm
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4.

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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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:
5.

図書

図書
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:
6.

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:
7.

図書

図書
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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8.

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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目次情報: 続きを見る
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
9.

図書

図書
by Daniel T. Finkbeiner, II ; drawings by Evan Gillespie
出版情報: San Francisco : W.H. Freeman , Tokyo : Charles E. Tuttle, 1960  vii, 248 p.: ill. ; 22 cm
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10.

図書

図書
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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