矩陣分析

內(nèi)容概要

　　本書旨在為讀者提供泛函分析的精髓矩陣分析。算子理論，算子代數(shù)，數(shù)學(xué)物理和數(shù)值分析專業(yè)的研究生和科研人員將對《矩陣分析》感興趣?！毒仃嚪治觯河⑽?影印版)》可以作為高等線性代數(shù)和矩陣分析方向的研究生基礎(chǔ)教程，也可以作為算子理論和數(shù)值分析方向的補(bǔ)充教程，包括的核心思想有最優(yōu)化理論，特征值的變分原理，算子單調(diào)性和凸分析，矩陣函數(shù)的擾動(dòng)和矩陣不等式。這些內(nèi)容大多數(shù)都是第一次以書中這么獨(dú)特的方式講述。讀者將會從書中學(xué)到很多強(qiáng)大的工具、廣泛的應(yīng)用技巧以及和數(shù)學(xué)專業(yè)其他領(lǐng)域之間的聯(lián)系。矩陣不等式使得《矩陣分析》對數(shù)值分析，數(shù)學(xué)物理和算子理論專業(yè)中學(xué)生，科研人員的參考價(jià)值凸顯。
讀者對象：適用于數(shù)學(xué)專業(yè)的研究生，科研人員以及最優(yōu)化感興趣的有關(guān)人員。

書籍目錄

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

圖書封面

評論、評分、閱讀與下載

---

    矩陣分析 PDF格式下載

---