矩阵分析（英文 影印版） 出版时间：2011年版 内容简介 《矩阵分析》旨在为读者提供泛函分析的精髓矩阵分析。算子理论，算子代数，数学物理和数值分析专业的研究生和科研人员将对《矩阵分析》感兴趣。《矩阵分析：英文（影印版）》可以作为高等线性代数和矩阵分析方向的研究生基础教程，也可以作为算子理论和数值分析方向的补充教程，包括的核心思想有最优化理论，特征值的变分原理，算子单调性和凸分析，矩阵函数的扰动和矩阵不等式。这些内容大多数都是第一次以《矩阵分析》中这么独特的方式讲述。读者将会从书中学到很多强大的工具、广泛的应用技巧以及和数学专业其他领域之间的联系。矩阵不等式使得《矩阵分析》对数值分析，数学物理和算子理论专业中学生，科研人员的参考价值凸显。 读者对象：适用于数学专业的研究生，科研人员以及最优化感兴趣的有关人员。 目录 preface i a review of linear algebra i.1 vector spaces and inner product spaces i.2 linear operators and matrices i.3 direct sums i.4 tensor products i.5 symmetry classes i.6 problems i.7 notes and references ii majorisation and doubly stochastic matrices ii.1 basic notions ii.2 birkhoff‘s theorem ii.3 convex and monotone functions ii.4 binary algebraic operations and majorisation ii.5 problems ii.6 notes and references iii variational principles for eigenvalues ili.1 the minimax principle for eigenvalues iii.2 weyl’s inequalities iii.3 wielandt‘s minimax principle iii.4 lidskii’s theorems iii.5 eigenvalues of real parts and singular values iii.6 problems iii.7 notes and references iv symmetric norms iv. 1 norms on cn iv.2 unitarily invariant norms on operators on cn iv.3 lidskii‘s theorem （third proof） iv.4 weakly unitarily invariant norms iv.5 problems iv.6 notes and references v operator monotone and operator convex functions v.1 definitions and simple examples v.2 some characterisations v.3 smoothness properties v.4 loewner’s theorems v.5 problems v.6 notes and references vi spectral variation of normal matrices vi.1 continuity of roots of polynomials vi.2 hermitian and skew-hermitian matrices vi.3 estimates in the operator norm vi.4 estimates in the probenius norm vi.5 geometry and spectral variation： the operator norm vi.6 geometry and spectral variation： wui norms vi.7 some inequalities for the determinant vi.8 problems vi.9 notes and references vii perturbation of spectral subspaces of normal matrices vii.1 pairs of subspaces vii.2 the equation ax - xb = y vii.3 perturbation of eigenspaces vii.4 a perturbation bound for eigenvalues vii.5 perturbation of the polar factors vii.6 appendix： evaluating the （fourier） constants vii.7 problems vii.8 notes and references viii spectral variation of nonnormal matrices viii.1 general spectral variation bounds viii.4 matrices with real eigenvalues viii.5 eigenvalues with symmetries viii.6 problems viii.7 notes and references ix a selection of matrix inequalities ix.1 some basic lemmas ix.2 products of positive matrices ix.3 inequalities for the exponential function ix.4 arithmetic-geometric mean inequalities ix.5 schwarz inequalities ix.6 the lieb concavity theorem ix.7 operator approximation ix.8 problems ix.9 notes and references x perturbation of matrix functions x.1 operator monotone functions x.2 the absolute value x.3 local perturbation bounds x.4 appendix： differential calculus x.5 problems x.6 notes and references references index
