（已有24条评价）基本信息
- 原书名：Topics in Matrix Analysis
- 原出版社： Cambridge University Press
- 作者： （美）Roger A.Horn,Charles R.Johnson
- 丛书名： 图灵原版数学·统计学系列
- 出版社：人民邮电出版社
- ISBN：7115140278
- 上架时间：2005-10-14
- 出版日期：2005 年10月
- 开本：16开
- 页码：592
- 版次：1-1
- 所属分类：数学 > 代数，数论及组合理论 > 矩阵论
教材 > 研究生/本科/专科教材 > 理学 > 数学
编辑推荐
本书是继《矩阵分析卷1》之后推出的矩阵领域又一经典之作，详尽讨论了卷1未能包括但又具有极高应用价值的论题。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。
内容简介
作译者
Roger A．Horn 线性代数和矩阵理论领域国际知名权威。1967年获得斯坦福大学数学博士，1972-1979年任约翰·霍普金斯大学数学系系主任，现为犹他大学教授。曾担任American Mathematical Monthly编辑。
Charies R．Johnson线性代数和矩阵理论领域国际知名权威。现为威廉玛丽学院教授。Johnson在学术界十分活跃，发表沦文近300篇，担任过多个主要矩阵分析类杂志的编辑和两份SIAM杂志的主编。由于他在数学科学领域作出厂杰出贡献而被授予华盛顿科学学会奖。
Charies R．Johnson线性代数和矩阵理论领域国际知名权威。现为威廉玛丽学院教授。Johnson在学术界十分活跃，发表沦文近300篇，担任过多个主要矩阵分析类杂志的编辑和两份SIAM杂志的主编。由于他在数学科学领域作出厂杰出贡献而被授予华盛顿科学学会奖。
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
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
前言
This volume is a sequel to the previously published Matriz Analysis and includes development of further topics that support applications of matrix theory. We refer the reader to the preface of the prior volume for many general comments that apply here also. We adopt the notation and referencing conventions of that volume and make specific reference to it [HJ] as needed.
Matriz Analysis developed the topics of broadest utility in the connection of matrix theory to other subjects and for modern research in the subject. The current volume develops a further set of slightly more specialized topics in the same spirit. These are: the field of values (or classical humericai range), matrix stability and inertia (including M-matrices), singular values and associated inequalities, matrix equations and Kronecker products, Hadamard (or entrywise) products of matrices, and several ways in which matrices and functions interact. Each of these topics is an area of active current research, and several of them do not yet enjoy a broad exposition elsewhere.
Though this book should serve as a reference for these topics, the exposition is designed for use in an advanced course. Chapters include motivational background, discussion, relations to other topics, and literature references. Most sections include exercises in the development as well as many problems that reinforce or extend the subject under discussion. There are, of course, other matrix analysis topics not developed here that warrant attention. Some of these already enjoy useful expositions; for example, totally positive matrices are discussed in [And] and [Kar].
We have included many exercises and over 650 problems because we feel they are essential to the development of an understanding of the subject and its implications. The exercises occur throughout the text as part of the
development of each section; they are generally elementary and of immediate use in understanding the concepts. We recommend that the reader work at least a broad selection of these. Problems are listed (in no particular order) at the end of sections; they cover a range of difficulties and types (from theoretical to computational) and they may extend the topic, develop special aspects, or suggest alternate proofs of major ideas.In order to enhance the utility of the book as a reference, many problems have hints;these are collected in a separate section following Chapter 6. The results of some problems are referred to in other problems or in the text itself. We cannot overemphasize the importance of the reader's active involvement in carrying out the exercises and solving problems.
As in the prior volume, a broad list of related books and major surveys is given prior to the index, and references to this list are given via mnemonic code in square brackets. Readers may find the reference list of independent utility.
We appreciate the assistance of our colleagues and students who have offered helpful suggestions or commented on the manuscripts that preceded publication of this volume. They include M. Bakonyi, W. Barrett, O. Chan,C. Cullen, M. Cusick, J. Dietrich, S. H. Friedberg, S. Gabriel, F. Hall, C.-K.Li, M. Lundquist, R. Mathias, D. Merino, R. Merris, P. Nylen, A. Sourour,G. W. Stewart, R. C. Thompson, P. van Dooren, and E. M. E. Wermuth.
The authors wish to maintain the utility of this volume to the community and welcome communication from readers of errors or omissions that they find. Such communications will be rewarded with a current copy of all known errata.
R. A. H.
C. R. J.
Matriz Analysis developed the topics of broadest utility in the connection of matrix theory to other subjects and for modern research in the subject. The current volume develops a further set of slightly more specialized topics in the same spirit. These are: the field of values (or classical humericai range), matrix stability and inertia (including M-matrices), singular values and associated inequalities, matrix equations and Kronecker products, Hadamard (or entrywise) products of matrices, and several ways in which matrices and functions interact. Each of these topics is an area of active current research, and several of them do not yet enjoy a broad exposition elsewhere.
Though this book should serve as a reference for these topics, the exposition is designed for use in an advanced course. Chapters include motivational background, discussion, relations to other topics, and literature references. Most sections include exercises in the development as well as many problems that reinforce or extend the subject under discussion. There are, of course, other matrix analysis topics not developed here that warrant attention. Some of these already enjoy useful expositions; for example, totally positive matrices are discussed in [And] and [Kar].
We have included many exercises and over 650 problems because we feel they are essential to the development of an understanding of the subject and its implications. The exercises occur throughout the text as part of the
development of each section; they are generally elementary and of immediate use in understanding the concepts. We recommend that the reader work at least a broad selection of these. Problems are listed (in no particular order) at the end of sections; they cover a range of difficulties and types (from theoretical to computational) and they may extend the topic, develop special aspects, or suggest alternate proofs of major ideas.In order to enhance the utility of the book as a reference, many problems have hints;these are collected in a separate section following Chapter 6. The results of some problems are referred to in other problems or in the text itself. We cannot overemphasize the importance of the reader's active involvement in carrying out the exercises and solving problems.
As in the prior volume, a broad list of related books and major surveys is given prior to the index, and references to this list are given via mnemonic code in square brackets. Readers may find the reference list of independent utility.
We appreciate the assistance of our colleagues and students who have offered helpful suggestions or commented on the manuscripts that preceded publication of this volume. They include M. Bakonyi, W. Barrett, O. Chan,C. Cullen, M. Cusick, J. Dietrich, S. H. Friedberg, S. Gabriel, F. Hall, C.-K.Li, M. Lundquist, R. Mathias, D. Merino, R. Merris, P. Nylen, A. Sourour,G. W. Stewart, R. C. Thompson, P. van Dooren, and E. M. E. Wermuth.
The authors wish to maintain the utility of this volume to the community and welcome communication from readers of errors or omissions that they find. Such communications will be rewarded with a current copy of all known errata.
R. A. H.
C. R. J.
