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1.

図書
図書
1. 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：
2.

図書
図書
2. 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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3.

図書
図書
3. 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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4.

図書
図書
4. Elementary linear algebra with supplemental applications. 11th ed (: pbk)
Howard Anton, Chris Rorres
出版情報: Hoboken, N.J. : John Wiley & Sons, c2015  xiii, 769 p. ; 26 cm
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5.

図書
図書
5. Elementary linear algebra with supplemental applications. 10th ed
Howard Anton, Chris Rorres
出版情報: Hoboken, N.J. : John Wiley & Sons, c2011  xiv, 777 p. ; 26 cm
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目次情報: 続きを見る
Systems of Linear Equations and Matrices / Chapter 1：
Determinants / Chapter 2：
Euclidean Vector Spaces / Chapter 3：
General Vector Spaces / Chapter 4：
Eignvalues and Eigenvectors / Chapter 5：
Inner Product Spaces / Chapter 6：
Diagonalization and Quadratic Forms / Chapter 7：
Linear Transformations / Chapter 8：
Numerical Methods / Chapter 9：
Applications of Linear Algebra / Chapter 10：
Systems of Linear Equations and Matrices / Chapter 1：
Determinants / Chapter 2：
Euclidean Vector Spaces / Chapter 3：
6.

図書
図書
6. Handbook of linear algebra. 2nd ed (: hardback)
edited by Leslie Hogben
出版情報: Boca Raton : CRC Press, Taylor & Fransis Group, c2014  1 v. (various paging) ; 26 cm
シリーズ名: Discrete mathematics and its applications / Kenneth H. Rosen, series editor
A Chapman & Hall book
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7.

図書
図書
7. Introduction to linear algebra. 5th ed
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge Press, c2016  x, 574 p. ; 24 cm
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目次情報: 続きを見る
Introduction to Vectors / 1：
Vectors and Linear Combinations / 1.1：
Lengths and Dot Products / 1.2：
Matrices / 1.3：
Solving Linear Equations / 2：
Vectors and Linear Equations / 2.1：
The Idea of Elimination / 2.2：
Elimination Using Matrices / 2.3：
Rules for Matrix Operations / 2.4：
Inverse Matrices / 2.5：
Elimination = Factorization: A = LU / 2.6：
Transposes and Permutations / 2.7：
Vector Spaces and Subspaces / 3：
Spaces of Vectors / 3.1：
The Nullspace of A: Solving Ax = 0 and Rx = 0 / 3.2：
The Complete Solution to Ax = b / 3.3：
Independence, Basis and Dimension / 3.4：
Dimensions of the Four Subspaces / 3.5：
Orthogonality / 4：
Orthogonality of the Four Subspaces / 4.1：
Projections / 4.2：
Least Squares Approximations / 4.3：
Orthonormal Bases and Gram-Schmidt / 4.4：
Determinants / 5：
The Properties of Determinants / 5.1：
Permutations and Cofactors / 5.2：
Cramer's Rule, Inverses, and Volumes / 5.3：
Eigenvalues and Eigenvectors / 6：
Introduction to Eigenvalues / 6.1：
Diagonalizing a Matrix / 6.2：
Systems of Differential Equations / 6.3：
Symmetric Matrices / 6.4：
Positive Definite Matrices / 6.5：
The Singular Value Decomposition (SVD) / 7：
Image Processing by Linear Algebra / 7.1：
Bases and Matrices in the SVD / 7.2：
Principal Component Analysis (PCA by the SVD) / 7.3：
The Geometry of the SVD / 7.4：
Linear Transformations / 8：
The Idea of a Linear Transformation / 8.1：
The Matrix of a Linear Transformation / 8.2：
The Search for a Good Basis / 8.3：
Complex Vectors and Matrices / 9：
Complex Numbers / 9.1：
Hermitian and Unitary Matrices / 9.2：
The Fast Fourier Transform / 9.3：
Applications / 10：
Graphs and Networks / 10.1：
Matrices in Engineering / 10.2：
Markov Matrices, Population, and Economics / 10.3：
Linear Programming / 10.4：
Fourier Series: Linear Algebra for Functions / 10.5：
Computer Graphics / 10.6：
Linear Algebra for Cryptography / 10.7：
Numerical Linear Algebra / 11：
Gaussian Elimination in Practice / 11.1：
Norms and Condition Numbers / 11.2：
Iterative Methods and Preconditioned / 11.3：
Linear Algebra in Probability & Statistics / 12：
Mean, Variance, and Probability / 12.1：
Covariance Matrices and Joint Probabilities / 12.2：
Multivariate Gaussian and Weighted Least Squares / 12.3：
Matrix Factorizations
Index
Sex Great Theorems/Linear Algebra in a Nutshell
Introduction to Vectors / 1：
Vectors and Linear Combinations / 1.1：
Lengths and Dot Products / 1.2：
8.

図書
図書
8. Linear algebra : step by step
Kuldeep Singh
出版情報: Oxford : Oxford University Press, 2014  viii, 608 p. ; 24 cm
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9.

図書
図書
9. Linear algebra : a modern introduction. 3rd ed (: pbk)
David Poole
出版情報: [Melbourne, Vic.,] : Brooks/Cole/Cengage Learning, c2011  xxvi, 726 p. ; 26 cm
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目次情報: 続きを見る
Vectors / 1：
Introduction: The Racetrack Game
The Geometry and Algebra of Vectors
Length and Angle: The Dot Product
Exploration: Vectors and Geometry
Lines and Planes
Exploration: The Cross Product
Applications: Force Vectors; Code Vectors
Vignette: The Codabar System
Systems of Linear Equations / 2：
Introduction: Triviality
Introduction to Systems of Linear Equations
Direct Methods for Solving Linear Systems
Exploration: Lies My Computer Told Me
Exploration: Partial Pivoting
Exploration: Counting Operations: An Introduction to the Analysis of Algorithms
Spanning Sets and Linear Independence
Applications: Allocation of Resources
Balancing Chemical Equations
Network Analysis
Electrical Networks
Linear Economic Models
Finite Linear Games
Vignette: The Global Positioning System
Iterative Methods for Solving Linear Systems
Matrices / 3：
Introduction: Matrices in Action
Matrix Operations
Matrix Algebra
The Inverse of a Matrix
The LU Factorization
Subspaces, Basis, Dimension, and Rank
Introduction to Linear Transformations
Vignette: Robotics
Applications: Markov Chains
Population Growth
Graphs and Digraphs
Error-Correcting Codes
Eigenvalues and Eigenvectors / 4：
Introduction: A Dynamical System on Graphs
Introduction to Eigenvalues and Eigenvectors
Determinants
Vignette: Lewis Carroll's Condensation Method
Exploration: Geometric Applications of Determinants
Eigenvalues and Eigenvectors of n x n Matrices
Similarity and Diagonalization
Iterative Methods for Computing Eigenvalues
Applications and the Perron-Frobenius Theorem: Markov Chains
The Perron-Frobenius Theorem
Linear Recurrence Relations
Systems of Linear Differential Equations
Discrete Linear Dynamical Systems
Vignette: Ranking Sports Teams and Searching the Internet
Orthogonality / 5：
Introduction: Shadows on a Wall
Orthogonality in Rn
Orthogonal Complements and Orthogonal Projections
The Gram-Schmidt Process and the QR Factorization
Exploration: The Modified QR Factorization
Exploration: Approximating Eigenvalues with the QR Algorithm
Orthogonal Diagonalization of Symmetric Matrices
Applications: Dual Codes
Quadratic Forms
Graphing Quadratic Equations
Vector Spaces / 6：
Introduction: Fibonacci in (Vector) Space
Vector Spaces and Subspaces
Linear Independence, Basis, and Dimension
Exploration: Magic Squares
Change of Basis
Linear Transformations
The Kernel and Range of a Linear Transformation
The Matrix of a Linear Transformation
Exploration: Tilings, Lattices and the Crystallographic Restriction
Applications: Homogeneous Linear Differential Equations
Linear Codes
Distance and Approximation / 7：
Introduction: Taxicab Geometry
Inner Product Spaces
Exploration: Vectors and Matrices with Complex Entries
Exploration: Geometric Inequalities and Optimization Problems
Norms and Distance Functions
Least Squares Approximation
The Singular Value Decomposition
Vignette: Digital Image Compression
Applications: Approximation of Functions
Mathematical Notation and Methods of Proof / Appendix A：
Mathematical Induction / Appendix B：
Complex Numbers / Appendix C：
Polynomials / Appendix D：
Vectors / 1：
Introduction: The Racetrack Game
The Geometry and Algebra of Vectors
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