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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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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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目次情報: 続きを見る
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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