矩阵分析

出版时间：2011-4  出版社：世界图书出版公司  作者：巴蒂亚  页数：347  

内容概要

　　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，科研人员以及最优化感兴趣的有关人员。

书籍目录

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

用户评论 (总计3条)

•   这本书内容丰富，比较实用。不过难度比较大（这其实是GTM系列的特点）。
•   是继续学习李群的基础
•   内容清晰,题量充足,先看看!