Roger A.Horn 线性代数和矩阵理论领域国际知名权威。1967年获得斯坦福大学数学博士,1972-1979年任约翰·霍普金斯大学数学系系主任,现为犹他大学教授。曾担任AMERICAN MATHE-MATICAL MONTHLY编辑。 Charles R.Johnson线性代数和矩阵理论领域国际知名权威。现为威廉
【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
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