close
1.

図書
図書
1. Linear algebra and its applications
Gilbert Strang
出版情報: New York : Academic Press, c1976  xi, 374 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Matrices and Gaussian Elimination / Chapter 1：
Introduction / 1.1：
The Geometry of Linear Equations / 1.2：
An Example of Gaussian Elimination / 1.3：
Matrix Notation and Matrix Multiplication / 1.4：
Triangular Factors and Row Exchanges / 1.5：
Inverses and Transposes / 1.6：
Special Matrices and Applications / 1.7：
Review Exercises: Chapter 1
Vector Spaces / Chapter 2：
Vector Spaces and Subspaces / 2.1：
Solving Ax = 0 and Ax = b / 2.2：
Linear Independence, Basis, and Dimension / 2.3：
The Four Fundamental Subspaces / 2.4：
Graphs and Networks / 2.5：
Linear Transformations / 2.6：
Review Exercises: Chapter 2
Orthogonality / Chapter 3：
Orthogonal Vectors and Subspaces / 3.1：
Cosines and Projections onto Lines / 3.2：
Projections and Least Squares / 3.3：
Orthogonal Bases and Gram-Schmidt / 3.4：
The Fast Fourier Transform / 3.5：
Review Exercises: Chapter 3
Determinants / Chapter 4：
Properties of the Determinant / 4.1：
Formulas for the Determinant / 4.3：
Applications of Determinants / 4.4：
Review Exercises: Chapter 4
Eigenvalues and Eigenvectors / Chapter 5：
Diagonalization of a Matrix / 5.1：
Difference Equations and Powers A[superscript k] / 5.3：
Differential Equations and e[superscript At] / 5.4：
Complex Matrices / 5.5：
Similarity Transformations / 5.6：
Review Exercises: Chapter 5
Positive Definite Matrices / Chapter 6：
Minima, Maxima, and Saddle Points / 6.1：
Tests for Positive Definiteness / 6.2：
Singular Value Decomposition / 6.3：
Minimum Principles / 6.4：
The Finite Element Method / 6.5：
Computations with Matrices / Chapter 7：
Matrix Norm and Condition Number / 7.1：
Computation of Eigenvalues / 7.3：
Iterative Methods for Ax = b / 7.4：
Linear Programming and Game Theory / Chapter 8：
Linear Inequalities / 8.1：
The Simplex Method / 8.2：
The Dual Problem / 8.3：
Network Models / 8.4：
Game Theory / 8.5：
Intersection, Sum, and Product of Spaces / Appendix A：
The Jordan Form / Appendix B：
Solutions to Selected Exercises
Matrix Factorizations
Matrices and Gaussian Elimination / Chapter 1：
Introduction / 1.1：
The Geometry of Linear Equations / 1.2：
2.

図書
図書
2. Introduction to linear algebra. 5th ed
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge Press, c2016  x, 574 p. ; 24 cm
所蔵情報: loading…
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：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼