- 矩阵分析
- - 作者：(印)巴蒂亚
  - 出版社：世界图书出版公司
  - ISBN：9787510033056
  - 出版日期：2011/04/01
  - 页数：347
- 售价：18

内容大纲
作者介绍
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

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作者介绍

目录

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