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矩阵分析 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （印）巴蒂亚著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510033056
- 出版时间：2011
- 标注页数：349页
- 文件大小：59MB
- 文件页数：361页
- 主题词：矩阵分析－研究生－教材－英文
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图书目录
Ⅰ A Review of Linear Algebra1
Ⅰ.1 Vector Spaces and Inner Product Spaces1
Ⅰ.2 Linear Operators and Matrices3
Ⅰ.3 Direct Sums9
Ⅰ.4 Tensor Products12
Ⅰ.5 Symmetry Classes16
Ⅰ.6 Problems20
Ⅰ.7 Notes and References26
Ⅱ Majorisation and Doubly Stochastic Matrices28
Ⅱ.1 Basic Notions28
Ⅱ.2 Birkhoff's Theorem36
Ⅱ.3 Convex and Monotone Functions40
Ⅱ.4 Binary Algebraic Operations and Majorisation48
Ⅱ.5 Problems50
Ⅱ.6 Notes and References54
Ⅲ Variational Principles for Eigenvalues57
Ⅲ.1 The Minimax Principle for Eigenvalues57
Ⅲ.2 Weyl's Inequalities62
Ⅲ.3 Wielandt's Minimax Principle65
Ⅲ.4 Lidskii's Theorems68
Ⅲ.5 Eigenvalues of Real Parts and Singular Values73
Ⅲ.6 Problems75
Ⅲ.7 Notes and References78
Ⅳ Symmetric Norms84
Ⅳ.1 Norms on Cn84
Ⅳ.2 Unitarily Invariant Norms on Operators on Cn91
Ⅳ.3 Lidskii's Theorem (Third Proof)98
Ⅳ.4 Weakly Unitarily Invariant Norms101
Ⅳ.5 Problems107
Ⅳ.6 Notes and References109
Ⅴ Operator Monotone and Operator Convex Functions112
Ⅴ.1 Definitions and Simple Examples112
Ⅴ.2 Some Characterisations117
Ⅴ.3 Smoothness Properties123
Ⅴ.4 Loewner's Theorems131
Ⅴ.5 Problems147
Ⅴ.6 Notes and References149
Ⅵ Spectral Variation of Normal Matrices152
Ⅵ.1 Continuity of Roots of Polynomials153
Ⅵ.2 Hermitian and Skew-Hermitian Matrices155
Ⅵ.3 Estimates in the Operator Norm159
Ⅵ.4 Estimates in the Frobenius Norm165
Ⅵ.5 Geometry and Spectral Variation:the Operator Norm.168
Ⅵ.6 Geometry and Spectral Variation:wui Norms173
Ⅵ.7 Some Inequalities for the Determinant181
Ⅵ.8 Problems184
Ⅵ.9 Notes and References190
Ⅶ Perturbation of Spectral Subspaces of Normal Matrices194
Ⅶ.1 Pairs of Subspaces195
Ⅶ.2 The Equation AX－XB=Y203
Ⅶ.3 Perturbation of Eigenspaces211
Ⅶ.4 A Perturbation Bound for Eigenvalues212
Ⅶ.5 Perturbation of the Polar Factors213
Ⅶ.6 Appendix: Evaluating the (Fourier) constants216
Ⅶ.7 Problems221
Ⅶ.8 Notes and References223
Ⅷ Spectral Variation of Nonnormal Matrices226
Ⅷ.1 General Spectral Variation Bounds227
Ⅷ.4 Matrices with Real Eigenvalues238
Ⅷ.5 Eigenvalues with Symmetries240
Ⅷ.6 Problems244
Ⅷ.7 Notes and References249
Ⅸ A Selection of Matrix Inequalities253
Ⅸ.1 Some Basic Lemmas253
Ⅸ.2 Products of Positive Matrices255
Ⅸ.3 Inequalities for the Exponential Function258
Ⅸ.4 Arithmetic-Geometric Mean Inequalities262
Ⅸ.5 Schwarz Inequalities266
Ⅸ.6 The Lieb Concavity Theorem271
Ⅸ.7 Operator Approximation275
Ⅸ.8 Problems279
Ⅸ.9 Notes and References285
Ⅹ Perturbation of Matrix Functions289
Ⅹ.1 Operator Monotone Functions289
Ⅹ.2 The Absolute Value296
Ⅹ.3 Local Perturbation Bounds301
Ⅹ.4 Appendix: Differential Calculus310
Ⅹ.5 Problems317
Ⅹ.6 Notes and References320
References325
Index339