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本帖最后由 raowy2009 于 2011-4-8 13:53 编辑
Matrix Mathematics 2nd Edition.part1.rar
(4.39 MB, 下载次数: 241 )
Matrix Mathematics 2nd Edition.part2.rar
(961.35 KB, 下载次数: 241 )
书名：Matrix Mathematics：Theory, Facts, and Formulas
作者：Dennis S. Bernstein
出版：PRINCETON UNIVERSITY PRESS，2009
版次：第二版
目录
Preface to the Second Edition xv
Preface to the First Edition xvii
Special Symbols xxi
Conventions, Notation, and Terminology xxxiii
1. Preliminaries 1
1.1 Logic and Sets 1
1.2 Functions 3
1.3 Relations 5
1.4 Graphs 8
1.5 Facts on Logic, Sets, Functions, and Relations 10
1.6 Facts on Graphs 13
1.7 Facts on Binomial Identities and Sums 14
1.8 Facts on Convex Functions 21
1.9 Facts on Scalar Identities and Inequalities in One Variable 22
1.10 Facts on Scalar Identities and Inequalities in Two Variables 30
1.11 Facts on Scalar Identities and Inequalities in Three Variables 39
1.12 Facts on Scalar Identities and Inequalities in Four Variables 46
1.13 Facts on Scalar Identities and Inequalities in Six Variables 47
1.14 Facts on Scalar Identities and Inequalities in Eight Variables 47
1.15 Facts on Scalar Identities and Inequalities in n Variables 48
1.16 Facts on Scalar Identities and Inequalities in 2n Variables 60
1.17 Facts on Scalar Identities and Inequalities in 3n Variables 67
1.18 Facts on Scalar Identities and Inequalities in Complex Variables 68
1.19 Facts on Trigonometric and Hyperbolic Identities 74
1.20 Notes 76
2. Basic Matrix Properties 77
2.1 Matrix Algebra 77
2.2 Transpose and Inner Product 84
2.3 Convex Sets, Cones, and Subspaces 89
2.4 Range and Null Space 93
2.5 Rank and Defect 95
2.6 Invertibility 98
2.7 The Determinant 102
2.8 Partitioned Matrices 106
2.9 Facts on Polars, Cones, Dual Cones, Convex Hulls, and Subspaces
110
2.10 Facts on Range, Null Space, Rank, and Defect 115
2.11 Facts on the Range, Rank, Null Space, and Defect of
Partitioned Matrices 120
2.12 Facts on the Inner Product, Outer Product, Trace, and Matrix
Powers 126
2.13 Facts on the Determinant 128
2.14 Facts on the Determinant of Partitioned Matrices 132
2.15 Facts on Left and Right Inverses 140
2.16 Facts on the Adjugate and Inverses 141
2.17 Facts on the Inverse of Partitioned Matrices 146
2.18 Facts on Commutators 149
2.19 Facts on Complex Matrices 151
2.20 Facts on Geometry 154
2.21 Facts on Majorization 162
2.22 Notes 164
3. Matrix Classes and Transformations 165
3.1 Matrix Classes 165
3.2 Matrices Based on Graphs 170
3.3 Lie Algebras and Groups 171
3.4 Matrix Transformations 173
3.5 Projectors, Idempotent Matrices, and Subspaces 175
3.6 Facts on Group-Invertible and Range-Hermitian Matrices 177
3.7 Facts on Normal, Hermitian, and Skew-Hermitian Matrices 178
3.8 Facts on Commutators 184
3.9 Facts on Linear Interpolation 185
3.10 Facts on the Cross Product 186
3.11 Facts on Unitary and Shifted-Unitary Matrices 189
3.12 Facts on Idempotent Matrices 198
3.13 Facts on Projectors 206
3.14 Facts on Reflectors 211
3.15 Facts on Involutory Matrices 212
3.16 Facts on Tripotent Matrices 212
3.17 Facts on Nilpotent Matrices 213
3.18 Facts on Hankel and Toeplitz Matrices 215
3.19 Facts on Hamiltonian and Symplectic Matrices 216
3.20 Facts on Miscellaneous Types of Matrices 217
3.21 Facts on Groups 221
3.22 Facts on Quaternions 225
3.23 Notes 229
4. Polynomial Matrices and Rational Transfer Functions 231
4.1 Polynomials 231
4.2 Polynomial Matrices 234
4.3 The Smith Decomposition and Similarity Invariants 236
4.4 Eigenvalues 239
4.5 Eigenvectors 245
4.6 The Minimal Polynomial 247
4.7 Rational Transfer Functions and the Smith-McMillan
Decomposition 249
4.8 Facts on Polynomials and Rational Functions 253
4.9 Facts on the Characteristic and Minimal Polynomials 260
4.10 Facts on the Spectrum 265
4.11 Facts on Graphs and Nonnegative Matrices 272
4.12 Notes 281
5. Matrix Decompositions 283
5.1 Smith Form 283
5.2 Multicompanion Form 283
5.3 Hypercompanion Form and Jordan Form 287
5.4 Schur Decomposition 292
5.5 Eigenstructure Properties 295
5.6 Singular Value Decomposition 301
5.7 Pencils and the Kronecker Canonical Form 304
5.8 Facts on the Inertia 307
5.9 Facts on Matrix Transformations for One Matrix 311
5.10 Facts on Matrix Transformations for Two or More Matrices 316
5.11 Facts on Eigenvalues and Singular Values for One Matrix 321
5.12 Facts on Eigenvalues and Singular Values for Two or More
Matrices 333
5.13 Facts on Matrix Pencils 338
5.14 Facts on Matrix Eigenstructure 338
5.15 Facts on Matrix Factorizations 345
5.16 Facts on Companion, Vandermonde, and Circulant Matrices 352
5.17 Facts on Simultaneous Transformations 358
5.18 Facts on the Polar Decomposition 359
5.19 Facts on Additive Decompositions 360
5.20 Notes 361
6. Generalized Inverses 363
6.1 Moore-Penrose Generalized Inverse 363
6.2 Drazin Generalized Inverse 367
6.3 Facts on the Moore-Penrose Generalized Inverse for One
Matrix 369
6.4 Facts on the Moore-Penrose Generalized Inverse for Two or
More Matrices 377
6.5 Facts on the Moore-Penrose Generalized Inverse for
Partitioned Matrices 385
6.6 Facts on the Drazin and Group Generalized Inverses 393
6.7 Notes 398
7. Kronecker and Schur Algebra 399
7.1 Kronecker Product 399
7.2 Kronecker Sum and Linear Matrix Equations 402
7.3 Schur Product 404
7.4 Facts on the Kronecker Product 405
7.5 Facts on the Kronecker Sum 409
7.6 Facts on the Schur Product 413
7.7 Notes 416
8. Positive-Semidefinite Matrices 417
8.1 Positive-Semidefinite and Positive-Definite Orderings 417
8.2 Submatrices 419
8.3 Simultaneous Diagonalization 422
8.4 Eigenvalue Inequalities 424
8.5 Exponential, Square Root, and Logarithm of Hermitian Matrices 430
8.6 Matrix Inequalities 431
8.7 Facts on Range and Rank 443
8.8 Facts on Structured Positive-Semidefinite Matrices 444
8.9 Facts on Identities and Inequalities for One Matrix 450
8.10 Facts on Identities and Inequalities for Two or More Matrices 456
8.11 Facts on Identities and Inequalities for Partitioned Matrices 467
8.12 Facts on the Trace 475
8.13 Facts on the Determinant 485
8.14 Facts on Convex Sets and Convex Functions 494
8.15 Facts on Quadratic Forms 500
8.16 Facts on Simultaneous Diagonalization 507
8.17 Facts on Eigenvalues and Singular Values for One Matrix 508
8.18 Facts on Eigenvalues and Singular Values for Two or More
Matrices 512
8.19 Facts on Alternative Partial Orderings 522
8.20 Facts on Generalized Inverses 525
8.21 Facts on the Kronecker and Schur Products 531
8.22 Notes 541
9. Norms 543
9.1 Vector Norms 543
9.2 Matrix Norms 546
9.3 Compatible Norms 549
9.4 Induced Norms 553
9.5 Induced Lower Bound 558
9.6 Singular Value Inequalities 560
9.7 Facts on Vector Norms 563
9.8 Facts on Matrix Norms for One Matrix 571
9.9 Facts on Matrix Norms for Two or More Matrices 580
9.10 Facts on Matrix Norms for Partitioned Matrices 593
9.11 Facts on Matrix Norms and Eigenvalues Involving One Matrix 596
9.12 Facts on Matrix Norms and Eigenvalues Involving Two or More
Matrices 599
9.13 Facts on Matrix Norms and Singular Values for One Matrix 602
9.14 Facts on Matrix Norms and Singular Values for Two or More
Matrices 607
9.15 Facts on Least Squares 618
9.16 Notes 619
10.Functions of Matrices and Their Derivatives 621
10.1 Open Sets and Closed Sets 621
10.2 Limits 622
10.3 Continuity 623
10.4 Derivatives 625
10.5 Functions of a Matrix 628
10.6 Matrix Square Root and Matrix Sign Functions 629
10.7 Matrix Derivatives 630
10.8 Facts Involving One Set 632
10.9 Facts Involving Two or More Sets 634
10.10 Facts on Matrix Functions 637
10.11 Facts on Functions and Derivatives 638
10.12 Notes 642
11.The Matrix Exponential and Stability Theory 643
11.1 Definition of the Matrix Exponential 643
11.2 Structure of the Matrix Exponential 646
11.3 Explicit Expressions 651
11.4 Matrix Logarithms 654
11.5 The Logarithm Function 656
11.6 Lie Groups 658
11.7 Lyapunov Stability Theory 660
11.8 Linear Stability Theory 662
11.9 The Lyapunov Equation 666
11.10 Discrete-Time Stability Theory 669
11.11 Facts on Matrix Exponential Formulas 671
11.12 Facts on the Matrix Sine and Cosine 677
11.13 Facts on the Matrix Exponential for One Matrix 677
11.14 Facts on the Matrix Exponential for Two or More Matrices 681
11.15 Facts on the Matrix Exponential and Eigenvalues,
Singular Values, and Norms for One Matrix 689
11.16 Facts on the Matrix Exponential and Eigenvalues,
Singular Values, and Norms for Two or More Matrices 692
11.17 Facts on Stable Polynomials 695
11.18 Facts on Stable Matrices 698
11.19 Facts on Almost Nonnegative Matrices 706
11.20 Facts on Discrete-Time-Stable Polynomials 708
11.21 Facts on Discrete-Time-Stable Matrices 712
11.22 Facts on Lie Groups 715
11.23 Facts on Subspace Decomposition 716
11.24 Notes 722
12.Linear Systems and Control Theory 723
12.1 State Space and Transfer Function Models 723
12.2 Laplace Transform Analysis 726
12.3 The Unobservable Subspace and Observability 727
12.4 Observable Asymptotic Stability 732
12.5 Detectability 734
12.6 The Controllable Subspace and Controllability 735
12.7 Controllable Asymptotic Stability 743
12.8 Stabilizability 747
12.9 Realization Theory 749
12.10 Zeros 757
12.11 H2 System Norm 765
12.12 Harmonic Steady-State Response 768
12.13 System Interconnections 770
12.14 Standard Control Problem 772
12.15 Linear-Quadratic Control 775
12.16 Solutions of the Riccati Equation 778
12.17 The Stabilizing Solution of the Riccati Equation 782
12.18 The Maximal Solution of the Riccati Equation 787
12.19 Positive-Semidefinite and Positive-Definite Solutions of the
Riccati Equation 789
12.20 Facts on Stability, Observability, and Controllability 790
12.21 Facts on the Lyapunov Equation and Inertia 793
12.22 Facts on Realizations and the H2 System Norm 798
12.23 Facts on the Riccati Equation 802
12.24 Notes 805
Bibliography 807
Author Index 891
Index 903 |
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发表于 2011-4-8 13:52:23
