A polynomial approach to linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 360 S. graph. Darst. |
| ISBN: | 0387946438 |
Internformat
MARC
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| 245 | 1 | 0 | |a A polynomial approach to linear algebra |c Paul A. Fuhrmann |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XIII, 360 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text | Contents
Preface vii
1 Preliminaries 1
1.1 Maps 1
1.2 Groups 3
1.3 Rings and Fields 8
1.4 Modules 28
1.5 Exercises 30
1.6 Notes and Remarks 32
2 Linear Spaces 33
2.1 Linear Spaces 33
2.2 Linear Combinations 35
2.3 Subspaces 35
2.4 Linear Dependence and Independence 37
2.5 Subspaces and Bases 40
2.6 Direct Sums 41
2.7 Quotient Spaces 43
2.8 Coordinates 45
2.9 Change of Basis Transformations 46
2.10 Lagrange Interpolation 48
2.11 Taylor Expansion 50
2.12 Exercises 51
2.13 Notes and Remarks 52
xii Contents
3 Determinants 53
3.1 Basic Properties 53
3.2 Cramer s Rule 58
3.3 The Sylvester Resultant 60
3.4 Exercises 62
3.5 Notes and Remarks 64
4 Linear Transformations 65
4.1 Linear Transformations 65
4.2 Matrix Representations 73
4.3 Linear Functionals and Duality 77
4.4 The Adjoint Transformation 84
4.5 Polynomial Module Structure on Vector Spaces 86
4.6 Exercises 95
4.7 Notes and Remarks 96
5 The Shift Operator 97
5.1 Basic Properties 97
5.2 Circulant Matrices 107
5.3 Rational Models 110
5.4 The Chinese Remainder Theorem 113
5.5 Hermite Interpolation 114
5.6 Duality 115
5.7 Reproducing Kernels 120
5.8 Exercises 123
5.9 Notes and Remarks 125
6 Structure Theory of Linear Transformations 127
6.1 Cyclic Transformations 127
6.2 The Invariant Factor Algorithm I34
6.3 Noncyclic Transformations 137
6.4 Diagonalization 141
6.5 Exercises 144
6.6 Notes and Remarks 149
7 Inner Product Spaces 1* 1
7.1 Geometry of Inner Product Spaces 151
7.2 Operators in Inner Product Spaces 157
7.3 Unitary Operators I60
7.4 Self Adjoint Operators 164
7.5 Singular Vectors and Singular Values 176
7.6 Unitary Embeddings 179
7.7 Exercises i83
7.8 Notes and Remarks 185
Contents xiii
8 Quadratic Forms 187
8.1 Preliminaries 187
8.2 Sylvester s Law of Inertia 190
8.3 Hankel Operators and Forms 196
8.4 Bezoutians 200
8.5 Representation of Bezoutians 204
8.6 Diagonalization of Bezoutians 208
8.7 Bezout and Hankel Matrices 215
8.8 Inversion of Hankel Matrices 221
8.9 Continued Fractions and Orthogonal Polynomials 228
8.10 The Cauchy Index 240
8.11 Exercises 245
8.12 Notes and Remarks 249
9 Stability 251
9.1 Root Location Using Quadratic Forms 251
9.2 Exercises 268
9.3 Notes and Remarks 269
10 Elements of System Theory 271
10.1 Introduction 271
10.2 Systems and Their Representations 272
10.3 Realization Theory 277
10.4 Stabilization 292
10.5 The Youla Kucera Parametrization 297
10.6 Exercises 300
10.7 Notes and Remarks 303
11 Hankel Norm Approximation 305
11.1 Introduction 305
11.2 Preliminaries 307
11.3 Schmidt Pairs of Hankel Operators 323
11.4 Duality and Hankel Norm Approximation 330
11.5 Nevanlinna Pick Interpolation 337
11.6 Hankel Approximant Singular Values 339
11.7 Exercises 349
11.8 Notes and Remarks 351
References 353
Index 357
|
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| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:00:47Z |
| institution | BVB |
| isbn | 0387946438 |
| language | English |
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| physical | XIII, 360 S. graph. Darst. |
| publishDate | 1996 |
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| spelling | Fuhrmann, Paul Abraham 1937- Verfasser (DE-588)141517077 aut A polynomial approach to linear algebra Paul A. Fuhrmann New York [u.a.] Springer 1996 XIII, 360 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Lineare Algebra - Lehrbuch Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007289017&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fuhrmann, Paul Abraham 1937- A polynomial approach to linear algebra Lineare Algebra - Lehrbuch Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | A polynomial approach to linear algebra |
| title_auth | A polynomial approach to linear algebra |
| title_exact_search | A polynomial approach to linear algebra |
| title_full | A polynomial approach to linear algebra Paul A. Fuhrmann |
| title_fullStr | A polynomial approach to linear algebra Paul A. Fuhrmann |
| title_full_unstemmed | A polynomial approach to linear algebra Paul A. Fuhrmann |
| title_short | A polynomial approach to linear algebra |
| title_sort | a polynomial approach to linear algebra |
| topic | Lineare Algebra - Lehrbuch Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra - Lehrbuch Algebras, Linear Lineare Algebra Lehrbuch |
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