Linear algebra and its applications: 2. More advanced
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Chichester u.a.
Horwood u.a.
1989
|
| Ausgabe: | 1. publ. |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 223 S. |
| ISBN: | 047021354X |
Internformat
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| 100 | 1 | |a Griffel, David H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear algebra and its applications |n 2. |p More advanced |c D. H. Griffel |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester u.a. |b Horwood u.a. |c 1989 | |
| 300 | |a X, 223 S. | ||
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Datensatz im Suchindex
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| adam_text | Table of Contents
PART IV MATRIX REPRESENTATIONS AND DIAGONALISATION
Chapter 9 Matrix Representation of Linear Transformations
9A Matrix Representations 3
9B Eigenvalue Problems 8
9C Change of Basis for Vectors 10
9D Change of Basis for Mappings 14
9E* Vector Spaces over Finite Fields and Error Correcting Codes ... 16
9F Proofs 21
Problems 23
Chapter 10 Similarity and Diagonalisation
10A Diagonalisation of Operators 26
10B Similarity of Matrices 28
IOC* Triangularisation of Operators 31
10D* Applications of the Triangular Form 32
10E Proofs 36
Problems 37
PART V INNER PRODUCTS AND SELF ADJOINT OPERATORS
Chapter 11 Inner Product Spaces
11A Real Inner Product Spaces 43
1 IB Geometry in Real Inner Product Spaces 47
HC Complex Inner Product Spaces 50
VI
11D Orthogonal Sets 54
HE Orthogonal Bases 56
11F Gram Schmidt Orthogonalisation 59
11G Change of Basis: Orthogonal and Unitary Matrices 61
11H* Orthogonal Complements 65
111* Adjoints and Linear Equations 68
11J* Adjoints of Linear Operators 71
UK* The QR Algorithm 74
11L Proofs of Theorems 78
Problems 80
Chapter 12 Self Adjoint Operators
12A Self Adjoint Operators 90
12B Orthogonal Diagonalisation 93
12C* Rayleigh s Principle 96
12D* Positive Definite Operators 102
12E* Positive Definite Matrices and Gaussian Elimination 105
12F* Extensions of the Diagonalisation Theorem 107
12G* Projectors 109
12H* Orthogonal Projectors 112
121* The Spectral Representation of a Self Adjoint Operator 116
12J* Eigenvalues and the Theory of Almost Singular Matrices .... 118
12K* Quantum Mechanics 119
12L Proof of the Spectral Theorem 124
Problems 126
PART VI FURTHER DEVELOPMENTS
Chapter 13 Least Squares, the Pseudo inverse, and Related Matters
13A Least Squares Approximation 137
13B Approximation in Inner Product Spaces and the Normal Equations 140
13C The Orthogonal Least Squares Method 143
13D The Singular Value Decomposition 144
13E The Singular Value Decomposition and Least Squares 148
13F The Pseudo inverse 150
13G Other Aspects of the Singular Value Decomposition 153
13H Generalized Inverses 156
Problems 159
Chapter 14 Duality and its Applications
14A Linear Functionals 166
14B Examples of Covectors 171
14C Duality 173
14D Duality in Inner Product Spaces 176
14E Transformation of Covectors 177
14F Orthogonality without Inner Products 179
14G Annihilators 180
14H Dual Operators 183
141 Duality and Linear Equations 184
14J The Theory of Vector Inequalities 187
14K Convexity and the Farkas Alternative 190
14L Duality in Linear Programming 193
14M Proofs of Theorems 198
Problems 199
Appendix I Closed sets 206
Solutions to Exercises 209
Hints and Answers to Selected Problems 213
References 219
Index 221
|
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| id | DE-604.BV002304346 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:42Z |
| institution | BVB |
| isbn | 047021354X |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001514451 |
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| spelling | Griffel, David H. Verfasser aut Linear algebra and its applications 2. More advanced D. H. Griffel 1. publ. Chichester u.a. Horwood u.a. 1989 X, 223 S. txt rdacontent n rdamedia nc rdacarrier (DE-604)BV002304317 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001514451&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griffel, David H. Linear algebra and its applications |
| title | Linear algebra and its applications |
| title_auth | Linear algebra and its applications |
| title_exact_search | Linear algebra and its applications |
| title_full | Linear algebra and its applications 2. More advanced D. H. Griffel |
| title_fullStr | Linear algebra and its applications 2. More advanced D. H. Griffel |
| title_full_unstemmed | Linear algebra and its applications 2. More advanced D. H. Griffel |
| title_short | Linear algebra and its applications |
| title_sort | linear algebra and its applications more advanced |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001514451&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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