作者：巴蒂亚
页数：347
出版社：世界图书出版公司
出版日期：2011
ISBN：9787510033056
电子书格式：pdf/epub/txt
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。
本书特色
巴蒂亚编著的《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会对本书感兴趣。本书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。
目录
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
