矩陣分析是由世界圖書出版公司在2011年出版的圖書，作者是巴蒂亞。
基本介紹
- 中文名：矩陣分析
- 別名：Matrix Analysis
- 作者：巴蒂亞
- 出版時間：2011年4月1日
- 出版社：世界圖書出版公司
- ISBN：9787510033056
內容簡介,圖書目錄,
內容簡介
《矩陣分析》旨在為讀者提供泛函分析的精髓矩陣分析。運算元理論，運算元代數，數學物理和數值分析專業的研究生和科研人員將對《矩陣分析》感興趣。《矩陣分析：英文》可以作為高等線性代數和矩陣分析方向的研究生基礎教程，也可以作為運算元理論和數值分析方向的補充教程，包括的核心思想有最最佳化理論，特徵值的變分原理，運算元單調性和凸分析，矩陣函式的擾動和矩陣不等式。這些內容大多數都是首次以《矩陣分析》中這么獨特的方式講述。讀者將會從書中學到很多強大的工具、廣泛的套用技巧以及和數學專業其他領域之間的聯繫。矩陣不等式使得《矩陣分析》對數值分析，數學物理和運算元理論專業中學生，科研人員的參考價值凸顯。
讀者對象：適用於數學專業的研究生，科研人員以及最佳化感興趣的有關人員。
圖書目錄
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
