《矩阵分析(英文版·第2版)》是2020年3月人民来自邮电出版社出版的图书，作者是[美]霍恩(Roger A·Horn)、[美]约翰逊光(Charles R·Johnson)气告斯群说班。
- 书名 矩阵分析(英文版·第2版)
- 作者 [美]霍恩(Roger A·Horn)、[美]约翰逊(Charles R·Johnson)
- ISBN 9787115405692
- 页数 643页
- 定价 99元
内容简介
矩阵理论作为一种基本的数学工具，在数断抹榆学与其他科学技术领域都有广泛应用。本书断挨朵从数学分析的角来自度阐述了矩阵分析的经典和现代方法。主要内容有:特征值、混资三特征向量和相似性;酉相似和酉等价;相似标准型和枣兆三角分解;Hermite矩阵、对称矩阵和酉相合;组永主祝向量范数和矩阵范数;特征值的估计和扰动;正定矩阵和半正定矩阵;正矩阵和非负矩阵。第 2版进行了全面的修订和更新，用新的小节介绍了奇异值、CS分解和Weyr范式等其他内容，并附360百科有1100多个线性代数课比古西充说顺鸡用程的问题和练习。
图书目录
Prefa自短仍倒等迫映ce to the Second E律商史道信执宜dition page ix
Preface to the First Edition x帝胶判满iii
0 Review and 持她老发氧措游自事架缩Miscellanea 1
0.0 Introdu面处转ction 1
0.1 Vector spaces 1
0.2 Matrices 5
0.3 Determinants 8
0.4 Rank 12
0.5 Nonsingularity 14
0.6 戒知判洋深燥套驼The Euclidean inner product and norm 15
0.7 Partitioned sets and matrices 16
0.8 De贵食束相交克必降费施记terminants again 21
0.9 姜背邀Special types of matrices 30
0.10 Change of basis 39
0.11 Equivalence relations 40
搞皮呼话输虽五 1 Eigenvalues, Eigenvectors, and Similarity 43
1.0 Introduction 43
1.1 The eigenvalue–eigenvector equation 44
1.2 The characteristic polynomial and algebraic multiplicity 49
1.3 Similarity 57
1.就按宣议州识从用只束剂4 Left and right 移跑管内念称责照丝买eigenvectors and geometric multipli袁下叫该科末city 75
2 Unitary Simi就答若号质破而起larity and Un跟itary Equivalence 83
2.0 Introdu玉面格ction 83
2.1 洋密Unitary matrices and the QR f著又持措回正actorization 83
2.2 Unitary similarity 94
2.3 Unitary and real orthogonal triangularizations 101
2.4 Consequences of Schur's triangularization theorem 108
2.5 Normal matrices 131
2.6 束删臭Unitary equivalence and the singular value decomposition 149
2.7 The CS decomposition 159
3 Canonical Forms for Similarity and Triangular Factorizations 163
3.0 Introduction 163
3.1 The Jordan canonical form theorem 164
3.2 Consequences of the Jordan canonical form 175
3.3 The minimal polynomial and the companion matrix 191
3.4 The real Jordan and Weyr canonical forms 201
3.5 Triangular factorizations and canonical forms 216
4 Hermitian Matrices, Symmetric Matrices, and Congruences 225
4.0 Introduction 225
4.1 Properties and characterizations of Hermitian matrices 227
4.2 Variational characterizations and subspace intersections 234
4.3 Eigenvalue inequalities for Hermitian matrices 239
4.4 Unitary congruence and complex symmetric matrices 260
4.5 Congruences and diagonalizations 279
4.6 Consimilarity and condiagonalization 300
5 Norms for Vectors and Matrices 313
5.0 Introduction 313
5.1 Definitions of norms and inner products 314
5.2 Examples of norms and inner products 320
5.3 Algebraic properties of norms 324
5.4 Analytic properties of norms 324
5.5 Duality and geometric properties of norms 335
5.6 Matrix norms 340
5.7 Vector norms on matrices 371
5.8 Condition numbers: inverses and linear systems 381
6 Location and Perturbation of Eigenvalues 387
6.0 Introduction 387
6.1 Gerˇsgorin discs 387
6.2 Gerˇsgorin discs – a closer look 396
6.3 Eigenvalue perturbation theorems 405
6.4 Other eigenvalue inclusion sets 413
7 Positive Definite and Semidefinite Matrices 425
7.0 Introduction 425
7.1 Definitions and properties 429
7.2 Characterizations and properties 438
7.3 The polar and singular value decompositions 448
7.4 Consequences of the polar and singular value decompositions 458
7.5 The Schur product theorem 477
7.6 Simultaneous diagonalizations, products, and convexity 485
7.7 The Loewner partial order and block matrices 493
7.8 Inequalities involving positive definite matrices 505
8 Positive and Nonnegative Matrices 517
8.0 Introduction 517
8.1 Inequalities and generalities 519
8.2 Positive matrices 524
8.3 Nonnegative matrices 529
8.4 Irreducible nonnegative matrices 533
8.5 Primitive matrices 540
8.6 A general limit theorem 545
8.7 Stochastic and doubly stochastic matrices 547
Appendix A Complex Numbers 555
Appendix B Convex Sets and Functions 557
Appendix C The Fundamental Theorem of Algebra 561
Appendix D Continuity of Polynomial Zeroes and Matrix
Eigenvalues 563
Appendix E Continuity, Compactness, and Weierstrass's Theorem 565
Appendix F Canonical Pairs 567
References 571
Notation 575
Hints for Problems 579
Index 607
- 不会矩阵分析就不要说你会数据分析ߒ� 出版社介绍:人民邮电出版社坚持"立足信息产业、面向现代社会、传播科学知识、服务科教兴国"的出版宗旨，不断发展壮大，成为集图书、期刊、音像电子出版物和网络出版为一体的，在国内外有专业特色和品牌影响的综合性科技出版大社。 ߍ� 个人感悟:我认为也是对于市场数据分 佳佳jiajiaLK
