英文共同题名：Topics in matrix analysis
副标题：无
作 者：(美)Roger A. Horn，(美)Charles R. Johnson著
分类号：O151.21
ISBN：9787115140272
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简介
本书在《矩阵分析卷1》基础之上，详尽叙述了卷1未能包括的但又具有极高应用价值的论题。这些论题包括：值域、稳定矩阵和惯性、奇异值、矩阵方程和kronecker乘积、hadamard乘积、矩阵和函数。
本书可作为数学及工程领域的研究生和研究人员的深入学习矩阵理论的教科书或参考书。
本书是继《矩阵分析卷1》之后推出的矩阵领域又一经典之作，详尽讨论了卷1未能包括但又具有极高应用价值的论题。
书中包含大量矩阵理论和线性代数方面的经典定理和推论，并给出了严格的证明。很多定理、推论、论题等都是本书所独有的，再加上作者精心组织，言简意赅的表述，造就了本书在矩阵领域不可比拟、独一无二的地位。
目录
Chapter 1 The field of values 1
1.0 Introduction 1
1.1 Definitions 5
1.2 Basic properties of the field of values 8
1.3 Convexity 17
1.4 Axiomatization 28
1.5 Location of the field of values 30
1.6 Geometry 48
1.7 Products of matrices 65
1.8 Generalizations of the field of values 77
Chapter 2 Stable matrices and inertia 89
2.0 Motivation 89
2.1 Definitions and elementary observations 91
2.2 Lyapunov's theorem 95
2.3 The Routh-Hurwitz conditions 101
2.4 Generalizations of Lyapunov's theorem 102
2.5 M-matrices, P-matrices, and related topics 112
Chapter 3 Singular value inequalities 134
3.0 Introduction and historical remarks 134
3.1 The singular value decomposition 144
3.2 Weak majorization and doubly substochastic matrices 163
3.3 Basic inequalities for singular values and eigenvalues 170
3.4 Sums of singular values: the Ky Fan k-norms 195
3.5 Singular values and unitarily invariant norms 203
3.6 Sufficiency of Weyl's product inequalities 217
3.7 Inclusion intervals for singular values 223
3.8 Singular value weak majorization for bilinear products 231
Chapter 4 Matrix equations and the Kronecker product 239
4.0 Motivation 239
4.1 Matrix equations 241
4.2 The Kronecker product 242
4.3 Linear matrix equations and Kronecker products 254
4.4 Kronecker sums and the equation AX + XB = C 268
4.5 Additive and multiplicative commutators and linear preservers 288
Chapter 5 The Hadamard product 298
5.0 Introduction 298
5.1 Some basic observations 304
5.2 The Schur product theorem 308
5.3 Generalizations of the Schur product theorem 312
5.4 The matrices A o (A-1) T and A o A-1 322
5.5 Inequalities for Hadamard products of general matrices: an overview 332
5.6 Singular values of a Hadamard product: a fundamental inequality 349
5.7 Hadamard products involving nonnegative matrices and M-matrices 356
Chapter 6 Matrices and functions 382
6.0 Introduction 382
6.1 Polynomial matrix functions and interpolation 383
6.2 Nonpolynomial matrix functions 407
6.3 Hadamard matrix functions 449
6.4 Square roots, logarithms, nonlinear matrix equations 459
6.5 Matrices of functions 490
6.6 A chain rule for functions of a matrix 520
Hints for problems 561
References 572
Notation 575
Index 580
1.0 Introduction 1
1.1 Definitions 5
1.2 Basic properties of the field of values 8
1.3 Convexity 17
1.4 Axiomatization 28
1.5 Location of the field of values 30
1.6 Geometry 48
1.7 Products of matrices 65
1.8 Generalizations of the field of values 77
Chapter 2 Stable matrices and inertia 89
2.0 Motivation 89
2.1 Definitions and elementary observations 91
2.2 Lyapunov's theorem 95
2.3 The Routh-Hurwitz conditions 101
2.4 Generalizations of Lyapunov's theorem 102
2.5 M-matrices, P-matrices, and related topics 112
Chapter 3 Singular value inequalities 134
3.0 Introduction and historical remarks 134
3.1 The singular value decomposition 144
3.2 Weak majorization and doubly substochastic matrices 163
3.3 Basic inequalities for singular values and eigenvalues 170
3.4 Sums of singular values: the Ky Fan k-norms 195
3.5 Singular values and unitarily invariant norms 203
3.6 Sufficiency of Weyl's product inequalities 217
3.7 Inclusion intervals for singular values 223
3.8 Singular value weak majorization for bilinear products 231
Chapter 4 Matrix equations and the Kronecker product 239
4.0 Motivation 239
4.1 Matrix equations 241
4.2 The Kronecker product 242
4.3 Linear matrix equations and Kronecker products 254
4.4 Kronecker sums and the equation AX + XB = C 268
4.5 Additive and multiplicative commutators and linear preservers 288
Chapter 5 The Hadamard product 298
5.0 Introduction 298
5.1 Some basic observations 304
5.2 The Schur product theorem 308
5.3 Generalizations of the Schur product theorem 312
5.4 The matrices A o (A-1) T and A o A-1 322
5.5 Inequalities for Hadamard products of general matrices: an overview 332
5.6 Singular values of a Hadamard product: a fundamental inequality 349
5.7 Hadamard products involving nonnegative matrices and M-matrices 356
Chapter 6 Matrices and functions 382
6.0 Introduction 382
6.1 Polynomial matrix functions and interpolation 383
6.2 Nonpolynomial matrix functions 407
6.3 Hadamard matrix functions 449
6.4 Square roots, logarithms, nonlinear matrix equations 459
6.5 Matrices of functions 490
6.6 A chain rule for functions of a matrix 520
Hints for problems 561
References 572
Notation 575
Index 580
英文共同题名：Topics in matrix analysis
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