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矩阵分析 卷1PDF|Epub|txt|kindle电子书版本网盘下载
- Roger A. Horn Charles R. Johnson 著
- 出版社： 北京：人民邮电出版社
- ISBN：9787115137685
- 出版时间：2005
- 标注页数：561页
- 文件大小：76MB
- 文件页数：575页
- 主题词：矩阵分析－英文
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图书目录
Chapter 0 Review and miscellanea1
0.0 Introduction1
0.1 Vector spaces1
0.2 Matrices4
0.3 Determinants7
0.4 Rank12
0.5 Nonsingularity14
0.6 The usual inner product14
0.7 Partitioned matrices17
0.8 Determinants again19
0.9 Special types of matrices23
0.10 Change of basis30
Chapter 1 Eigenvalues,eigenvectors,and similarity33
1.0 Introduction33
1.1 The eigenvalue-eigenvector equation34
1.2 The characteristic polynomial38
1.3 Similarity44
1.4 Eigenvectors57
Chapter 2 Unitary equivalence and normal matrices65
2.0 Introduction65
2.1 Unitary matrices66
2.2 Unitary equivalence72
2.3 Schur's unitary triangularization theorem79
2.4 Some implications of Schur's theorem85
2.5 Normal matrices100
2.6 QR factorization and algorithm112
Chapter 3 Canonical forms119
3.0 Introduction119
3.1 The Jordan canonical form:a proof121
3.2 The Jordan canonical form:some observations and applications129
3.3 Polynomials and matrices:the minimal polynomial142
3.4 Other canonical forms and factorizations150
3.5 Triangular factorizations158
Chapter 4 Hermitian and symmetric matrices167
4.0 Introduction167
4.1 Definitions,properties,and characterizations of Hermitian matrices169
4.2 Variational characterizations of eigenvalues of Hermitian matrices176
4.3 Some applications of the variational characterizations181
4.4 Complex symmetric matrices201
4.5 Congruence and simultaneous diagonalization of Hermitian and symmetric matrices218
4.6 Consimilarity and condiagonalization244
Chapter 5 Norms for vectors and matrices257
5.0 Introduction257
5.1 Defining properties of vector norms and inner products259
5.2 Examples of vector norms264
5.3 Algebraic properties of vector norms268
5.4 Analytic properties of vector norms269
5.5 Geometric properties of vector norms281
5.6 Matrix norms290
5.7 Vector norms on matrices320
5.8 Errors in inverses and solutions of linear systems335
Chapter 6 Location and perturbation of eigenvalues343
6.0 Introduction343
6.1 Ger？gorin discs344
6.2 Ger？gorin discs-a closer look353
6.3 Perturbation theorems364
6.4 Other inclusion regions378
Chapter 7 Positive definite matrices391
7.0 Introduction391
7.1 Definitions and properties396
7.2 Characterizations402
7.3 The polar form and the singular value decomposition411
7.4 Examples and applications of the singular value decomposition427
7.5 The Schur product theorem455
7.6 Congruence:products and simultaneous diagonalization464
7.7 The positive semidefinite ordering469
7.8 Inequalities for positive definite matrices476
Chapter 8 Nonnegative matrices487
8.0 Introduction487
8.1 Nonnegative matrices-inequalities and generalities490
8.2 Positive matrices495
8.3 Nonnegative matrices503
8.4 Irreducible nonnegative matrices507
8.5 Primitive matrices515
8.6 A general limit theorem524
8.7 Stochastic and doubly stochastic matrices526
Appendices531
A Complex numbers531
B Convex sets and functions533
C The fundamental theorem of algebra537
D Continuous dependence of the zeroes of a polynomial on its coefficients539
E Weierstrass's theorem541
References543
Notation547
Index549