Matrix analysis and applied linear algebra

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Matrix analysis and applied linear algebra / Carl Meyer

資料種別:: 図書
出版情報:: Philadelphia : Society for Industrial and Applied Mathematics (SIAM), c2000
形態:: 2 v. ; 25 cm. + 1 CD-ROM. (12 cm.)
著者名:: Meyer, Carl
ISBN:: 9780898714548 [0898714540] (: set)
書誌ID:: BA47363806

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注記:

Includes bibliographical references and index

主題:

Algebras, Linear; Matrices

言語:

英語

目次情報:

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：

Gaussian Elimination and Matrices / 1.2：

Gauss-Jordan Method / 1.3：

Two-Point Boundary Value Problems / 1.4：

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