中文名: 矩陣分析中的若干論題
原名: Topics in Matrix Analysis
作者: (美)Roger A.Horn,Charles R.Johnson
資源格式: DJVU
版本: 掃描版
出版社: Cambridge University Press
書號: 0521467136
發行時間: 1994年
地區: 美國
語言: 英文
簡介:

內容簡介:
本書是繼《矩陣分析》之後推出的矩陣領域又一經典之作，詳盡敘述了其未能包括的但又具有極高應用價值的論題。這些論題包括：值域、穩定矩陣和慣性、奇異值、矩陣方程和Kronecker乘積、Hadamard乘積、矩陣和函數。
本書可作為數學及工程領域的研究生和研究人員的深入學習矩陣理論的教科書或參考書。
書中包含大量矩陣理論和線性代數方面的經典定理和推論，並給出了嚴格的證明。很多定理、推論、論題等都是本書所獨有的，再加上作者精心組織，言簡意赅的表述，造就了本書在矩陣領域不可比擬、獨一無二的地位。
內容截圖:

目錄:
Chapter 1 The field of values
1.0 Introduction
1.1 Definitions
1.2 Basic properties of the field of values
1.3 Convexity
1.4 Axiomatization
1.5 Location of the field of values
1.6 Geometry
1.7 Products of matrices
i.8 Generalizations of the field of values
Chapter 2 Stable matrices and inertia
2.0 Motivation
2.1 Definitions and elementary observations
2.2 Lyapunov's theorem
2.3 The Routh-Hurwitz conditions
2.4 Generalizations of Lyapunov's theorem
2.5 M-matrices, P-matrices, and related topics
Chapter 3 Singular value inequalities
3.0 Introduction and historical remarks
3.1 The singular value decomposition
3.2 Weak majorization and doubly substochastic matrices
3.3 Basic inequalities for singular values and eigenvalues
3.4 Sums of singular values: the Ky Fan K-norms
3.5 Singular values and unitarily invariant norms
3.6 Sufficiency of Weyl's product inequalities
3.7 Inclusion intervals for singular values
3.8 Singular value weak majorization for bilinear products
Chapter 4 Matrix equations and the Kronecker product
4.0 Motivation
4.1 Matrix equations
4.2 The Kronecker product
4.3 Linear matrix equations and Kronecker products
4.4 Kronecker sums and the equation AX + XB=C
4.5 Additive and multiplicative commutators and linear
preservers
Chapter 5 The Hadamard product
5.0 Introduction
5.1 Some basic observations
5.2 The Schuf product theorem
5.3 Generalizations of the Schur product theorem
5.4 The matrices A o (A-1) T and A o A-1
5.5 Inequalities for Hadamard products of general matrices:an overview
5.6 Singular values of a Hadamard product: a fundamental inequality
5.7 Hadamard products involving nonnegative matrices and M-matrices
Chapter 6 Matrices and functions
6.0 Introduction
6.1 Polynomial matrix functions and interpolation
6.2 Nonpolynomial matrix functions
6.3 Hadamard matrix functions
6.4 Square roots, logarithms, nonlinear matrix equations
6.5 Matrices of functions
6.6 A chain rule for functions of a matrix
Hints for problems
References
Notation
Index