中文名: 矩陣分析
原名: 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: 0521386322
發行時間: 1990年
地區: 美國
語言: 英文
簡介:

內容簡介:
本書從數學分析的角度闡述了矩陣分析的經典和現代方法，不僅包括由於數學分析的需要而產生的線性代數的論題，還廣泛選擇了其他相關學科如微分方程、最優化、逼近理論、工程學和運籌學等有關的論題。本書主要內容有：特征值、特征向量和相似性、酉相似、Schur三角化及其推論、正規矩陣、標准形和包括Jordan標准形在內的各種分解、LU分解、QR分解和酉矩陣、Hermite矩陣和復對稱矩陣、向量范數和矩陣范數、特征值的估計和擾動、正定矩陣、非負矩陣。
本書由美國著名數學家R.A.Horn教授和C．R．Johnson教授合著，是矩陣理論方面的經典著作，原書自1985年出版以來，已經重印了10余次。書中論述了矩陣分析的經典方法和現代方法，不僅涵蓋了幾乎所有的基礎理論，還廣泛地對涉及其他相關學科的各種論題進行了有效的闡述，並對有關論題提供了現代的參考資料。
本書邏輯清晰，結構嚴謹，既注重教學又注重應用。在每一章的開始，作者都介紹幾個應用來引入本章的論題以激發學習興趣。在章節末尾，作者還獨具匠心地編排了許多具有探索性和啟發性的習題，引導讀者提高描述和解決數學問題的能力。所以不論是對從事線性代數純理論研究還是從事應用研究的人員，本書都是一本必備的參考書。
本書可作為理工科專業研究生或數學專業高年級本科生教材，也可供數學工作者和科技人員參考。
內容截圖:

目錄:
Contents
Chapter 0 Review and miscellanea 1
0.0 Introduction 1
0.1 Vector spaces 1
0.2 Matrices 4
0.3 Determinants 7
0.4 Rank 12
0.5 Nonsingularity 14
0.6 The usual inner product 14
0.7 Partitioned matrices 17
0.8 Determinants again 19
0.9 Special types of matrices 23
0.10 Change of basis 30
Chapter 1 Eigenvalues, eigenvectors, and similarity 33
1.0 Introduction 33
1.1 The eigenvalue-eigenvector equation 34
1.2 The characteristic polynomial 38
1.3 Similarity 44
1.4 Eigenvectors 57
Chapter 2 Unitary equivalence and normal matrices 65
2.0 Introduction 65
2.1 Unitary matrices 66
2.2 Unitary equivalence 72
2.3 Schur's unitary triangularizat ervations and applications 129
3.3 Polynomials and matrices: the minimal polynomial 142
3.4 Other canonical forms and factorizations 150
3.5 Triangular factorizations 158
Chapter 4 Hermitian and symmetric matrices 167
4.0 Introduction 167
4.1 Definitions, properties, and characterizations of Hermitian matrices 169
4.2 Variational characterizations of eigenvalues of Hermitian matrices 176
4.3 Some applications of the variational characterizations 181
4.4 Complex symmetric matrices 201
4.5 Congruence and simultaneous diagonalization of Hermitian and symmetric matrices 218
4.6 Consimilarity and condiagonalization 244
Chapter 5 Norms for vectors and matrices 257
5.0 Introduction 257
5.1 Defining properties of vector norms and inner products 259
5.2 Examples of vector norms 264
5.3 Algebraic properties of vector norms 268
5.4 Analytic properties of vector norms 269
5.5 Geometric properties of vector norms 281
5.6 Matrix norms 290
5.7 Vector norms on matrices 320
5.8 Errors in inverses and solutions of linear systems 335
Chapter 6 Location and perturbation of eigenvalues 343
6.0 Introduction 343
6.1 Gergorin discs 344
6.2 Gergorin discs - a closer look 353
6.3 Perturbation theorems 364
6.4 Other inclusion regions 378
Chapter 7 Positive definite matrices 391
7.0 Introduction 391
7.1 Definitions and properties 396
7.2 Characterizations 402
7.3 The polar form and the singular value decomposition 411
7.4 Examples and applications of the singular value decomposition 427
7.5 The Schur product theorem 455
7.6 Congruence: products and simultaneous diagonalization 464
7.7 The positive semidefinite ordering 469
7.8 Inequalities for positive definite matrices 476
Chapter 8 Nonnegative matrices 487
8.0 Introduction 487
8.1 Nonnegative matrices - inequalities and generalities 490
8.2 Positive matrices 495
8.3 Nonnegative matrices 503
8.4 Irreducible nonnegative matrices 507
8.5 Primitive matrices 515
8.6 A general limit theorem 524
8.7 Stochastic and doubly stochastic matrices 526
Appendices
A Complex numbers 531
B Convex sets and functions 533
C The fundamental theorem of algebra 537
D Continuous dependence of the zeroes of a olynomial on its coefficients 539
E Weierstrass's theorem 541
References 543
Notation 547
Index 549