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1.

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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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
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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3.

図書

図書
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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4.

図書

図書
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:
5.

図書

図書
Howard Anton, Chris Rorres
出版情報: Hoboken, N.J. : John Wiley & Sons, c2015  xiii, 769 p. ; 26 cm
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6.

図書

図書
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
7.

図書

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

図書

図書
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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9.

図書

図書
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:
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