矩陣分析（卷2）

內(nèi)容概要

　　本書在《矩陣分析 卷1》基礎(chǔ)之上，詳盡敘述了卷1未能包括的又具有極高應(yīng)用價值的論題。這些論題包括：值域、穩(wěn)定矩陣和慣性、奇異值、矩陣議程和kronecker乘積、Hadamard乘積、矩陣和函數(shù)。　　本書可作為數(shù)學(xué)及工程領(lǐng)域的研究生和研究人員的深入學(xué)習(xí)矩陣理論的教科書或參考書。

作者簡介

Roger A.Horn 線性代數(shù)和矩陣理論領(lǐng)域國際知名權(quán)威。1967年獲得斯坦福大學(xué)數(shù)學(xué)博士，1972-1979年任約翰·霍普金斯大學(xué)數(shù)學(xué)系系主任，現(xiàn)為猶他大學(xué)教授。曾擔任AMERICAN MATHE-MATICAL MONTHLY編輯。
    Charles R.Johnson線性代數(shù)和矩陣理論領(lǐng)域國際知名權(quán)威。現(xiàn)為威廉

書籍目錄

Chapter 1  The field of values　11.0　Introduction　11.1　Definitions　51.2　Basic properties of the field of values　81.3　Convexity　171.4　Axiomatization　281.5　Location of the field of values　301.6　Geometry　481.7　Products of matrices　651.8　Generalizations of the field of values　77Chapter 2  Stable matrices and inertia　892.0　Motivation　892.1　Definitions and elementary observations　912.2　Lyapunov's theorem　952.3　The Routh-Hurwitz conditions　1012.4　Generalizations of Lyapunov's theorem　1022.5　M-matrices, P-matrices, and related topics　112Chapter 3  Singular value inequalities　1343.0　Introduction and historical remarks　1343.1　The singular value decomposition　1443.2　Weak majorization and doubly substochastic matrices　1633.3　Basic inequalities for singular values and eigenvalues　1703.4　Sums of singular values: the Ky Fan k-norms　1953.5　Singular values and unitarily invariant norms　2033.6　Sufficiency of Weyl's product inequalities　2173.7　Inclusion intervals for singular values　2233.8　Singular value weak majorization for bilinear products　231Chapter 4  Matrix equations and the Kronecker product　2394.0　Motivation　2394.1　Matrix equations　2414.2　The Kronecker product　2424.3　Linear matrix equations and Kronecker products　2544.4　Kronecker sums and the equation AX + XB = C　2684.5　Additive and multiplicative commutators and linear preservers　288Chapter 5 The Hadamard product　2985.0　Introduction　2985.1　Some basic observations　3045.2　The Schur product theorem　3085.3　Generalizations of the Schur product theorem　3125.4　The matrices A o (A-1) T and A o A-1　3225.5　Inequalities for Hadamard products of general matrices: an overview　3325.6　Singular values of a Hadamard product: a fundamental inequality　3495.7　Hadamard products involving nonnegative matrices and M-matrices　356Chapter 6  Matrices and functions　3826.0　Introduction　3826.1　Polynomial matrix functions and interpolation　3836.2　Nonpolynomial matrix functions　4076.3　Hadamard matrix functions　4496.4　Square roots, logarithms, nonlinear matrix equations　4596.5　Matrices of functions　4906.6　A chain rule for functions of a matrix　520Hints for problems　561References　572Notation　575Index　580

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