Matrix analysis
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1999
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| Ausgabe: | Repr. |
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Datensatz im Suchindex
| _version_ | 1819614971095416832 |
|---|---|
| adam_text | MATRIX ANALYSIS ROGER A. HORN THE JOHNS HOPKINS UNIVERSITY CHARLES R.
JOHNSON COLLEGE OF WILLIAM AND MARY CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE PAGE IX CHAPTER 0 REVIEW AND MISCELLANEA 1 0.0 INTRODUCTION 1 1
4 7 12 14 14 17 19 23 30 33 33 34 38 44 57 CHAPTER 2 UNITARY EQUIVALENCE
AND NORMAL MATRICES 65 2.0 INTRODUCTION 65 2.1 UNITARY MATRICES 66 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.10 VECTOR SPACES MATRICES DETERMINANTS
RANK NONSINGULARITY THE USUAL INNER PRODUCT PARTITIONED MATRICES
DETERMINANTS AGAIN SPECIAL TYPES OF MATRICES CHANGE OF BASIS CHAPTER 1
EIGENVALUES, EIGENVECTORS, AND SIMILARITY 1.0 1.1 1.2 1.3 1.4
INTRODUCTION THE EIGENVALUE-EIGENVECTOR EQUATION THE CHARACTERISTIC
POLYNOMIAL SIMILARITY EIGENVECTORS VI CONTENTS 2.2 UNITARY EQUIVALENCE
72 2.3 SCHUR S UNITARY TRIANGULARIZATION THEOREM 79 2.4 SOME
IMPLICATIONS OF SCHUR S THEOREM 85 2.5 NORMAL MATRICES 100 2.6 QR
FACTORIZATION AND ALGORITHM 112 CHAPTER 3 CANONICAL FORMS 119 3.0
INTRODUCTION 119 3.1 THE JORDAN CANONICAL FORM: A PROOF 121 3.2 THE
JORDAN CANONICAL FORM: SOME OBSERVATIONS AND APPLICATIONS 129 3.3
POLYNOMIALS AND MATRICES: THE MINIMAL POLYNOMIAL 142 3.4 OTHER CANONICAL
FORMS AND FACTORIZATIONS 150 3.5 TRIANGULAR FACTORIZATIONS 158 CHAPTER 4
HERMITIAN AND SYMMETRIC MATRICES 167 4.0 INTRODUCTION 167 4.1
DEFINITIONS, PROPERTIES, AND CHARACTERIZATIONS OF HERMITIAN MATRICES 169
4.2 VARIATIONAL CHARACTERIZATIONS OF EIGENVALUES OF HERMITIAN MATRICES
176 4.3 SOME APPLICATIONS OF THE VARIATIONAL CHARACTERIZATIONS 181 4.4
COMPLEX SYMMETRIC MATRICES 201 4.5 CONGRUENCE AND SIMULTANEOUS
DIAGONALIZATION OF HERMITIAN AND SYMMETRIC MATRICES 218 4.6
CONSIMILARITY AND CONDIAGONALIZATION 244 CHAPTER 5 NORMS FOR VECTORS AND
MATRICES 257 5.0 INTRODUCTION 257 5.1 DEFINING PROPERTIES OF VECTOR
NORMS AND INNER PRODUCTS 259 5.2 EXAMPLES OF VECTOR NORMS 264 5.3
ALGEBRAIC PROPERTIES OF VECTOR NORMS 268 5.4 ANALYTIC PROPERTIES OF
VECTOR NORMS 269 5.5 GEOMETRIC PROPERTIES OF VECTOR NORMS 281 5.6 MATRIX
NORMS 290 5.7 VECTOR NORMS ON MATRICES 320 5.8 ERRORS IN INVERSES AND
SOLUTIONS OF LINEAR SYSTEMS 335 CONTENTS VII CHAPTER 6 LOCATION AND
PERTURBATION OF EIGENVALUES 343 6.0 INTRODUCTION 343 6.1 GERSGORIN DISCS
344 6.2 GERSGORIN DISCS - A CLOSER LOOK 353 6.3 PERTURBATION THEOREMS
364 6.4 OTHER INCLUSION REGIONS 378 CHAPTER 7 POSITIVE DEFINITE MATRICES
391 7.0 INTRODUCTION 391 7.1 DEFINITIONS AND PROPERTIES 396 7.2
CHARACTERIZATIONS 402 7.3 THE POLAR FORM AND THE SINGULAR VALUE
DECOMPOSITION 411 7.4 EXAMPLES AND APPLICATIONS OF THE SINGULAR VALUE
DECOMPOSITION 427 7.5 THE SCHUR PRODUCT THEOREM 455 7.6 CONGRUENCE:
PRODUCTS AND SIMULTANEOUS DIAGONALIZATION 464 7.7 THE POSITIVE
SEMIDEFINITE ORDERING 469 7.8 INEQUALITIES FOR POSITIVE DEFINITE
MATRICES 476 CHAPTER 8 NONNEGATIVE MATRICES 487 8.0 INTRODUCTION 487 8.1
NONNEGATIVE MATRICES - INEQUALITIES AND GENERALITIES 490 8.2 POSITIVE
MATRICES 495 8.3 NONNEGATIVE MATRICES 503 8.4 IRREDUCIBLE NONNEGATIVE
MATRICES 507 8.5 PRIMITIVE MATRICES 515 8.6 A GENERAL LIMIT THEOREM 524
8.7 STOCHASTIC AND DOUBLY STOCHASTIC MATRICES 526 APPENDICES A COMPLEX
NUMBERS 531 B CONVEX SETS AND FUNCTIONS 533 C THE FUNDAMENTAL THEOREM OF
ALGEBRA 537 D CONTINUOUS DEPENDENCE OF THE ZEROES OF A POLYNOMIAL ON ITS
COEFFICIENTS 539 E WEIERSTRASS S THEOREM 541 REFERENCES 543 NOTATION 547
INDEX 549
|
| any_adam_object | 1 |
| author | Horn, Roger A. 1942- Johnson, Charles R. 1948- |
| author_GND | (DE-588)142437808 (DE-588)143876384 |
| author_facet | Horn, Roger A. 1942- Johnson, Charles R. 1948- |
| author_role | aut aut |
| author_sort | Horn, Roger A. 1942- |
| author_variant | r a h ra rah c r j cr crj |
| building | Verbundindex |
| bvnumber | BV013978177 |
| ctrlnum | (OCoLC)178969195 (DE-599)BVBBV013978177 |
| edition | Repr. |
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| id | DE-604.BV013978177 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:45:18Z |
| institution | BVB |
| isbn | 0521305861 0521386322 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009568387 |
| oclc_num | 178969195 |
| open_access_boolean | |
| owner | DE-29T DE-355 DE-BY-UBR |
| owner_facet | DE-29T DE-355 DE-BY-UBR |
| physical | XIII, 561 S graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Horn, Roger A. 1942- Johnson, Charles R. 1948- Matrix analysis Lineare Algebra - Matrix <Mathematik> Matrizenanalysis (DE-588)4227735-8 gnd Matrizenrechnung (DE-588)4126963-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4227735-8 (DE-588)4126963-9 (DE-588)4037968-1 |
| title | Matrix analysis |
| title_auth | Matrix analysis |
| title_exact_search | Matrix analysis |
| title_full | Matrix analysis Roger A. Horn ; Charles R. Johnson |
| title_fullStr | Matrix analysis Roger A. Horn ; Charles R. Johnson |
| title_full_unstemmed | Matrix analysis Roger A. Horn ; Charles R. Johnson |
| title_short | Matrix analysis |
| title_sort | matrix analysis |
| topic | Lineare Algebra - Matrix <Mathematik> Matrizenanalysis (DE-588)4227735-8 gnd Matrizenrechnung (DE-588)4126963-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Lineare Algebra - Matrix <Mathematik> Matrizenanalysis Matrizenrechnung Matrix Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009568387&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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