《矩阵分析中的若干论题》Topics.in.Matrix.Analysis(Roger.A.Horn,Charles.R.Johnson)【djvu】

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内容简介:

本书是继《矩阵分析》之后推出的矩阵领域又一经典之作,详尽叙述了其未能包括的但又具有极高应用价值的论题。这些论题包括:值域、稳定矩阵和惯性、奇异值、矩阵方程和Kronecker乘积、Hadamard乘积、矩阵和函数。

本书可作为数学及工程领域的研究生和研究人员的深入学习矩阵理论的教科书或参考书。

书中包含大量矩阵理论和线性代数方面的经典定理和推论,并给出了严格的证明。很多定理、推论、论题等都是本书所独有的,再加上作者精心组织,言简意赅的表述,造就了本书在矩阵领域不可比拟、独一无二的地位。

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目录

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

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