| Physical description |
xii, 718 pages : illustrations ; 25 cm + 1 computer optical disc (4 3/4 in.) |
| Bibliography |
Includes bibliographical references and index. |
| Notes |
Also available with solutions manual. |
| Contents |
1. Linear Equations 1 -- 1.2 Gaussian Elimination and Matrices 3 -- 1.3 Gauss-Jordan Method 15 -- 1.4 Two-Point Boundary Value Problems 18 -- 1.5 Making Gaussian Elimination Work 21 -- 1.6 Ill-Conditioned Systems 33 -- 2. Rectangular Systems and Echelon Forms 41 -- 2.1 Row Echelon Form and Rank 41 -- 2.2 Reduced Row Echelon Form 47 -- 2.3 Consistency of 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 Why Do 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 Elementary Matrices and Equivalence 131 -- 3.10 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 Unitary and Orthogonal Matrices 320 -- 5.7 Orthogonal Reduction 341 -- 5.8 Discrete Fourier Transform 356 -- 5.9 Complementary Subspaces 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 Why Least 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 Elementary Properties of Eigensystems 489 -- 7.2 Diagonalization by Similarity Transformations 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 -- 8.2 Positive Matrices 663 -- 8.3 Nonnegative Matrices 670 -- 8.4 Stochastic Matrices and Markov Chains 687. |
| Subject |
Algebras, Linear.
|
|
Matrices.
|
| ISBN |
0898714540 |
|
