Matrix analysis for scientists & engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM
2005
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 157 S. graph. Darst. |
| ISBN: | 0898715768 9780898715767 |
Internformat
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Datensatz im Suchindex
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| adam_text | MATRIX ANALYSIS FOR SCIENTISTS & ENGINEERS ALAN J. LAUB UNIVERSITY OF
CALIFORNIA DAVIS, CALIFORNIA CONTENTS PREFACE XI 1 INTRODUCTION AND
REVIEW 1 1.1 SOME NOTATION AND TERMINOLOGY 1 1.2 MATRIX ARITHMETIC 3 1.3
INNER PRODUCTS AND ORTHOGONALITY 4 1.4 DETERMINANTS 4 2 VECTOR SPACES 7
2.1 DEFINITIONS AND EXAMPLES 7 2.2 SUBSPACES 9 2.3 LINEAR INDEPENDENCE
10 2.4 SUMS AND INTERSECTIONS OF SUBSPACES 13 3 LINEAR TRANSFORMATIONS
17 3.1 DEFINITION AND EXAMPLES 17 3.2 MATRIX REPRESENTATION OF LINEAR
TRANSFORMATIONS 18 3.3 COMPOSITION OF TRANSFORMATIONS . . . . . 19 3.4
STRUCTURE OF LINEAR TRANSFORMATIONS . . 20 3.5 FOUR FUNDAMENTAL
SUBSPACES 22 4 INTRODUCTION TO THE MOORE-PENROSE PSEUDOINVERSE 29 4.1
DEFINITIONS AND CHARACTERIZATIONS 29 4.2 EXAMPLES 30 4.3 PROPERTIES AND
APPLICATIONS 31 5 INTRODUCTION TO THE SINGULAR VALUE DECOMPOSITION 35
5.1 THE FUNDAMENTAL THEOREM 35 5.2 SOME BASIC PROPERTIES 38 5.3 ROW AND
COLUMN COMPRESSIONS 40 6 LINEAR EQUATIONS 43 6.1 VECTOR LINEAR EQUATIONS
43 6.2 MATRIX LINEAR EQUATIONS 44 6.3 A MORE GENERAL MATRIX LINEAR
EQUATION 47 6.4 SOME USEFUL AND INTERESTING INVERSES 47 VII VIII
CONTENTS 7 PROJECTIONS, INNER PRODUCT SPACES, AND NORMS 51 7.1
PROJECTIONS 51 7.1.1 THE FOUR FUNDAMENTAL ORTHOGONAL PROJECTIONS 52 7.2
INNER PRODUCT SPACES 54 7.3 VECTOR NORMS 57 7.4 MATRIX NORMS 59 8 LINEAR
LEAST SQUARES PROBLEMS 65 8.1 THE LINEAR LEAST SQUARES PROBLEM 65 8.2
GEOMETRIC SOLUTION 67 8.3 LINEAR REGRESSION AND OTHER LINEAR LEAST
SQUARES PROBLEMS 67 8.3.1 EXAMPLE: LINEAR REGRESSION 67 8.3.2 OTHER
LEAST SQUARES PROBLEMS 69 8.4 LEAST SQUARES AND SINGULAR VALUE
DECOMPOSITION 70 8.5 LEAST SQUARES AND QR FACTORIZATION 71 9 EIGENVALUES
AND EIGENVECTORS 75 9.1 FUNDAMENTAL DEFINITIONS AND PROPERTIES 75 9.2
JORDAN CANONICAL FORM 82 9.3 DETERMINATION OF THE JCF 85 9.3.1
THEORETICAL COMPUTATION 86 9.3.2 ON THE +L S IN JCF BLOCKS 88 9.4
GEOMETRIC ASPECTS OF THE JCF 89 9.5 THE MATRIX SIGN FUNCTION 91 10
CANONICAL FORMS 95 10.1 SOME BASIC CANONICAL FORMS 95 10.2 DEFINITE
MATRICES 99 10.3 EQUIVALENCE TRANSFORMATIONS AND CONGRUENCE 102 10.3.1
BLOCK MATRICES AND DEFINITENESS 104 10.4 RATIONAL CANONICAL FORM 104 11
LINEAR DIFFERENTIAL AND DIFFERENCE EQUATIONS 109 11.1 DIFFERENTIAL
EQUATIONS .109 11.1.1 PROPERTIES OF THE MATRIX EXPONENTIAL 109 11.1.2
HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS 112 11.1.3 INHOMOGENEOUS
LINEAR DIFFERENTIAL EQUATIONS 112 11.1.4 LINEAR MATRIX DIFFERENTIAL
EQUATIONS 113 11.1.5 MODAL DECOMPOSITIONS 114 11.1.6 COMPUTATION OF THE
MATRIX EXPONENTIAL 114 11.2 DIFFERENCE EQUATIONS 118 11.2.1 HOMOGENEOUS
LINEAR DIFFERENCE EQUATIONS 118 11.2.2 INHOMOGENEOUS LINEAR DIFFERENCE
EQUATIONS 118 11.2.3 COMPUTATION OF MATRIX POWERS . * 119 11.3
HIGHER-ORDER EQUATIONS 120 CONTENTS IX 12 GENERALIZED EIGENVALUE
PROBLEMS 125 12.1 THE GENERALIZED EIGENVALUE/EIGENVECTOR PROBLEM 125
12.2 CANONICAL FORMS 127 12.3 APPLICATION TO THE COMPUTATION OF SYSTEM
ZEROS 130 12.4 SYMMETRIC GENERALIZED EIGENVALUE PROBLEMS 131 12.5
SIMULTANEOUS DIAGONALIZATION 133 12.5.1 SIMULTANEOUS DIAGONALIZATION VIA
SVD 133 12.6 HIGHER-ORDER EIGENVALUE PROBLEMS 135 12.6.1 CONVERSION TO
FIRST-ORDER FORM 135 13 KRONECKER PRODUCTS 139 13.1 DEFINITION AND
EXAMPLES 139 13.2 PROPERTIES OF THE KRONECKER PRODUCT 140 13.3
APPLICATION TO SYLVESTER AND LYAPUNOV EQUATIONS . . . . 144 BIBLIOGRAPHY
151 INDEX 153
|
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| indexdate | 2024-07-09T20:05:39Z |
| institution | BVB |
| isbn | 0898715768 9780898715767 |
| language | English |
| lccn | 2004059962 |
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| physical | XIII, 157 S. graph. Darst. |
| publishDate | 2005 |
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| spelling | Laub, Alan J. 1948- Verfasser (DE-588)115244735 aut Matrix analysis for scientists & engineers Alan J. Laub Philadelphia SIAM 2005 XIII, 157 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier aMatrices aMathematical analysis Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Matrizentheorie (DE-588)4128970-5 s DE-604 Matrix Mathematik (DE-588)4037968-1 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013092636&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laub, Alan J. 1948- Matrix analysis for scientists & engineers aMatrices aMathematical analysis Matrix Mathematik (DE-588)4037968-1 gnd Matrizentheorie (DE-588)4128970-5 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4128970-5 (DE-588)4151278-9 |
| title | Matrix analysis for scientists & engineers |
| title_auth | Matrix analysis for scientists & engineers |
| title_exact_search | Matrix analysis for scientists & engineers |
| title_full | Matrix analysis for scientists & engineers Alan J. Laub |
| title_fullStr | Matrix analysis for scientists & engineers Alan J. Laub |
| title_full_unstemmed | Matrix analysis for scientists & engineers Alan J. Laub |
| title_short | Matrix analysis for scientists & engineers |
| title_sort | matrix analysis for scientists engineers |
| topic | aMatrices aMathematical analysis Matrix Mathematik (DE-588)4037968-1 gnd Matrizentheorie (DE-588)4128970-5 gnd |
| topic_facet | aMatrices aMathematical analysis Matrix Mathematik Matrizentheorie Einführung |
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