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