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Matrix analysis

Author: Horn, Roger A. ; Johnson, Charles R.Publisher: Cambridge University Press (CUP) 1985.Language: EnglishDescription: 561 p. ; 24 cm.ISBN: 9780521386326Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA155 .H67 1985
(Browse shelf)
001242560
Available 001242560
Total holds: 0

Includes bibliographical references and index

Digitized

Matrix Analysis Contents Preface Chapter 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 usual inner product 0.7 Partitioned matrices 0.8 Determinants again 0.9 Special types of matrices 0.10 Change of basis Chapter 1 Eigenvalues, eigenvectors, and similarity 1.0 Introduction 1.1 The eigenvalue-eigenvector equation 1.2 The characteristic polynomial 1.3 Similarity 1.4 Eigenvectors Chapter 2 Unitary equivalence and normal matrices 2.0 Introduction 2.1 Unitary matrices page ix 1 1 1 4 7 12 14 14 17 19 23 30 33 33 34 38 44 57 65 65 66 2.2 2.3 2.4 2.5 2.6 Unitary equivalence Schur's unitary triangularization theorem Some implications of Schur's theorem Normal matrices QR factorization and algorithm 72 79 85 100 112 119 119 121 129 142 150 158 167 167 169 176 181 201 218 244 257 257 259 264 268 269 281 290 320 335 Chapter 3 Canonical forms 3.0 Introduction 3.1 The Jordan canonical form: a proof 3.2 The Jordan canonical form: some observations and applications 3.3 Polynomials and matrices: the minimal polynomial 3.4 Other canonical forms and factorizations 3.5 Triangular factorizations Chapter 4 Hermitian and symmetric matrices 4.0 Introduction 4.1 Definitions, properties, and characterizations of Hermitian matrices 4.2 Variational characterizations of eigenvalues of Hermitian matrices 4.3 Some applications of the variational characterizations 4.4 Complex symmetric matrices 4.5 Congruence and simultaneous diagonalization of Hermitian and symmetric matrices 4.6 Consimilarity and condiagonalization Chapter 5 Norms for vectors and matrices 5.0 Introduction 5.1 Defining properties of vector norms and inner products 5.2 Examples of vector norms 5.3 Algebraic properties of vector norms 5.4 Analytic properties of vector norms 5.5 Geometric properties of vector norms 5.6 Matrix norms 5.7 Vector norms on matrices 5.8 Errors in inverses and solutions of linear systems Chapter 6 Location and perturbation of eigenvalues 6.0 Introduction 6.1 Gersgorin discs 6.2 Gersgorin discs - a closer look 6.3 Perturbation theorems 6.4 Other inclusion regions Chapter 7 Positive definite matrices 7.0 Introduction 7.1 Definitions and properties 7.2 Characterizations 7.3 The polar form and the singular value decomposition 7.4 Examples and applications of the singular value decomposition 7.5 The Schur product theorem 7.6 Congruence: products and simultaneous diagonalization 7.7 The positive semidefinite ordering 7.8 Inequalities for positive definite matrices Chapter 8 Nonnegative matrices 8.0 Introduction 8.1 Nonnegative matrices - 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 Appendices A B C D E References Notation Index Complex numbers Convex sets and functions The fundamental theorem of algebra Continuous dependence of the zeroes of a polynomial on its coefficients Weierstrass's theorem 343 343 344 353 364 378 391 391 396 402 411 427 455 464 469 476 487 487 490 495 503 507 515 524 526 531 533 537 539 541 543 547 549

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