Matrix Analysis 2nd edition by Roger Horn, Charles Johnson – Ebook PDF Instant Download/Delivery: 0521548233 , 978-0521548236
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ISBN 10: 0521548233
ISBN 13: 978-0521548236
Author: Roger Horn, Charles Johnson
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: – New sections on the singular value and CS decompositions – New applications of the Jordan canonical form – A new section on the Weyr canonical form – Expanded treatments of inverse problems and of block matrices – A central role for the Von Neumann trace theorem – A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair – Expanded index with more than 3,500 entries for easy reference – More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid – A new appendix provides a collection of problem-solving hints.
Matrix Analysis 2nd Table of contents:
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 Geršgorin discs
6.2 Geršgorin 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 singularvalue 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
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Tags: Roger Horn, Charles Johnson, Matrix Analysis