Introduction to linear algebra

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Introduction to linear algebra / Gilbert Strang

版:: 5th ed
資料種別:: 図書
出版情報:: Wellesley, Mass. : Wellesley-Cambridge Press, c2016
形態:: x, 574 p. ; 24 cm
著者名:: Strang, Gilbert, 1934- <DA00732202>
ISBN:: 9780980232776 [0980232775]
書誌ID:: BB21759525

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注記:

Includes index

主題:

Algebras, Linear

言語:

英語

目次情報:

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：

Matrices / 1.3：

Solving Linear Equations / 2：

Vectors and Linear Equations / 2.1：

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