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Matrix analysis and applied linear algebra

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Table of contents:
Preface ix
1. Linear Equations 1
1.1 Introduction 1
1.2 Gaussian Elimination and Matrices 3
1.3 Gauss–Jordan Method 15
1.4 Two-Point BoundaryV alue Problems 18
1.5 Making Gaussian Elimination Work 21
1.6 Ill-Conditioned Systems 3

2. Rectangular Systems and Echelon Forms 41
2.1 Row Echelon Form and Rank 41
2.2 Reduced Row Echelon Form 47
2.3 Consistencyof Linear Systems 53
2.4 Homogeneous Systems 57
2.5 Nonhomogeneous Systems 64
2.6 Electrical Circuits 73

3. Matrix Algebra 79
3.1 From Ancient China to Arthur Cayley 79
3.2 Addition and Transposition 81
3.3 Linearity 89
3.4 WhyDo It This Way 93
3.5 Matrix Multiplication 95
3.6 Properties of Matrix Multiplication 105
3.7 Matrix Inversion 115
3.8 Inverses of Sums and Sensitivity 124
3.9 ElementaryMatrices and Equivalence 131
3.10 The LU Factorization 141

4. Vector Spaces 159
4.1 Spaces and Subspaces 159
4.2 Four Fundamental Subspaces 169
4.3 Linear Independence 181
4.4 Basis and Dimension ............. 194
4.5 More about Rank 210
4.6 Classical Least Squares 223
4.7 Linear Transformations 238
4.8 Change of Basis and Similarity 251
4.9 Invariant Subspaces 259

5. Norms, Inner Products, and Orthogonality 269
5.1 Vector Norms 269
5.2 Matrix Norms 279
5.3 Inner-Product Spaces 286
5.4 Orthogonal Vectors 294
5.5 Gram–Schmidt Procedure 307
5.6 Unitaryand Orthogonal Matrices 320
5.7 Orthogonal Reduction 341
5.8 Discrete Fourier Transform 356
5.9 ComplementarySubspaces 383
5.10 Range-Nullspace Decomposition 394
5.11 Orthogonal Decomposition 403
5.12 Singular Value Decomposition 411
5.13 Orthogonal Projection 429
5.14 WhyLeast Squares? 446
5.15 Angles between Subspaces 450

6. Determinants 459
6.1 Determinants 459
6.2 Additional Properties of Determinants 475

7. Eigenvalues and Eigenvectors 489
7.1 ElementaryProp erties of Eigensystems 489
7.2 Diagonalization bySimilarit yT ransformations 505
7.3 Functions of Diagonalizable Matrices 525
7.4 Systems of Differential Equations 541
7.5 Normal Matrices 547
7.6 Positive Definite Matrices 558
7.7 Nilpotent Matrices and Jordan Structure 574
7.8 Jordan Form 587
7.9 Functions of Nondiagonalizable Matrices ..... 599
7.10 Difference Equations, Limits, and Summability 616
7.11 Minimum Polynomials and Krylov Methods 642

8. Perron–Frobenius Theory 661
8.1 Introduction 661
8.2 Positive Matrices 663
8.3 Nonnegative Matrices 670
8.4 Stochastic Matrices and Markov Chains 687

Contents vii Index ...................... 705

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Availability

Detail Information

Series Title

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Call Number

512.5 MEY m

Publisher

Philadelphia : Siam., 2000

Collation

xii, 718 hal.; ilus.; 24 cm + 1 CD

Language

English

ISBN/ISSN

9780898714548

Classification

512.5

Content Type

-

Media Type

-

Carrier Type

-

Edition

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Subject(s)

Algebras, Linear
Aljabar Linier

Specific Detail Info

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Statement of Responsibility

Carl D. Meyer

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