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矩阵分析

版次：1
页数：
字数：
印刷时间：2011年04月01日
开本：24开
纸张：胶版纸
包装：平装
是否套装：否
国际标准书号ISBN：9787510033056

作者:（印）巴蒂亚　著出版社:世界图书出版公司出版时间:2011年04月

内容简介

　　本书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*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书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*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

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

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