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

图书封面

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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!
 

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