Roger A. Horn
国际知名数学权威，现任美国犹他大学数学系研究教授，曾任约翰霍普金斯大学数学系系主任，并曾任American Mathematical Monthly编辑。
Charles R. Johnson
国际知名数学权威，现任美国威廉玛丽学院教授。因其在数学科学领域的杰出贡献被授予华盛顿科学学会奖。
目錄：
Preface to the Second Edition page
Preface to the First Edition
0 Review and Miscellanea
0.0 Introduction
0.1 Vector spaces
0.2 Matrices
0.3 Determinants
0.4 Rank
0.5 Nonsingularity
0.6 The Euclidean inner product and norm
0.7 Partitioned sets and matrices
0.8 Determinants again
0.9 Special types of matrices
0.10 Change of basis
0.11 Equivalence relations
1 Eigenvalues, Eigenvectors, and Similarity
1.0 Introduction
1.1 The eigenvalue–eigenvector equation
1.2 The characteristic polynomial and algebraic multiplicity
1.3 Similarity
1.4 Left and right eigenvectors and geometric multiplicity
2 Unitary Similarity and Unitary Equivalence
2.0 Introduction
2.1 Unitary matrices and the QR factorization
2.2 Unitary similarity
2.3 Unitary and real orthogonal triangularizations
2.4 Consequences of Schur’s triangularization theorem
2.5 Normal matrices
2.6 Unitary equivalence and the singular value decomposition
2.7 The CS decomposition
3 Canonical Forms for Similarity and Triangular Factorizations
3.0 Introduction
3.1 The Jordan canonical form theorem
3.2 Consequences of the Jordan canonical form
3.3 The minimal polynomial and the companion matrix
3.4 The real Jordan and Weyr canonical forms
3.5 Triangular factorizations and canonical forms
4 Hermitian Matrices, Symmetric Matrices, and Congruences
4.0 Introduction
4.1 Properties and characterizations of Hermitian matrices
4.2 Variational characterizations and subspace intersections
4.3 Eigenvalue inequalities for Hermitian matrices
4.4 Unitary congruence and complex symmetric matrices
4.5 Congruences and diagonalizations
4.6 Consimilarity and condiagonalization
5 Norms for Vectors and Matrices
5.0 Introduction
5.1 Definitions of norms and inner products
5.2 Examples of norms and inner products
5.3 Algebraic properties of norms
5.4 Analytic properties of norms
5.5 Duality and geometric properties of norms
5.6 Matrix norms
5.7 Vector norms on matrices
5.8 Condition numbers: inverses and linear systems
6 Location and Perturbation of Eigenvalues
6.0 Introduction
6.1 Gergorin discs
6.2 Gergorin discs – a closer look
6.3 Eigenvalue perturbation theorems
6.4 Other eigenvalue inclusion sets
7 Positive Definite and Semidefinite Matrices
7.0 Introduction
7.1 Definitions and properties
7.2 Characterizations and properties
7.3 The polar and singular value decompositions
7.4 Consequences of the polar and singular value decompositions
7.5 The Schur product theorem
7.6 Simultaneous diagonalizations, products, and convexity
7.7 The Loewner partial order and block matrices
7.8 Inequalities involving positive definite matrices
8 Positive and Nonnegative Matrices
8.0 Introduction
8.1 Inequalities and generalities
8.2 Positive matrices
8.3 Nonnegative matrices
8.4 Irreducible nonnegative matrices
8.5 Primitive matrices
8.6 A general limit theorem
8.7 Stochastic and doubly stochastic matrices
Appendix A Complex Numbers
Appendix B Convex Sets and Functions
Appendix C The Fundamental Theorem of Algebra
Appendix D Continuity of Polynomial Zeroes and Matrix Eigenvalues
Appendix E Continuity, Compactness, andWeierstrass’s Theorem
Appendix F Canonical Pairs
References
Notation
Hints for Problems
Index
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