Matrices and linear transformations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, MA u.a.
Addison-Wesley
1972
|
| Edition: | 2. ed. |
| Series: | Addison-Wesley series in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 318 S. |
| ISBN: | 020101209X |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS
Chapter I Matrices and Linear Systems
1.1 Introduction 1
1.2 fields and number systems 5
1.3 Matrices 10
1.4 Matrix addition and scalar multiplication 22
1.5 Transposition 27
1.6 Partitioned matrices 31
1.7 Special kinds of matrices 37
1.8 Row equivalence 41
1.9 f lemcntary matrices and matrix inverses 49
1.10 Column equivalence 57
I.I I Hquivalence 60
Chapter 2 Vector Spaces
2.1 Introduction 67
2.2 Subspaces 73
2 3 I inear independence and bases 78
2.4 The rank of a matrix 87
2.5 Coordinates and isomorphisms 93
2.6 Uniqueness theorem for row equivalence 102
Chapter 3 Determinants
3.1 Definition of the determinant 104
3.2 The Laplace expansion 108
3.3 Adjoints and inverses 117
3.4 Determinants and rank 122
Chapter 4 Linear Transformations
4.1 Definition and examples 124
4.2 Matrix representation 129
xl
xii Contents
4.3 Products and inverses 135
4.4 Change of basis and similarity 138
4.5 Characteristic vectors and characteristic values 143
4.6 Orthogonality and length 154
4.7 Gram Schmidt process 160
4.8 Schur s theorem and normal matrices 166
Chapter 5 Similarity: Part I
5.1 The Cayley Hamilton theorem 175
5.2 Direct sums and invariant subspaces 183
5.3 Nilpotent linear operators 189
5.4 The Jordan canonical form 195
5.5 Jordan form—continued 200
5.6 Commutativity (the equation AX = XB) 207
Chapter 6 Polynomials and Polynomial Matrices
6.1 Introduction and review 215
6.2 Divisibility and irreducibility 217
6.3 Lagrange interpolation 220
6.4 Matrices with polynomial elements 224
6.5 Equivalence over [x 228
6.6 Equivalence and similarity 231
Chapter 7 Similarity.: Part II
7.1 Nonderogatory matrices 236
7.2 Elementary divisors 240
7.3 The classical canonical form 244
7.4 Spectral decomposition 248
7.5 Polar decomposition 251
Chapter 8 Matrix Analysis
8.1 Sequences and series 255
8.2 Primary functions 260
8.3 Matrices of functions 265
8.4 Systems of linear differential equations 268
Chapter 9 Numerical Methods
9.1 Introduction 272
9.2 Exact methods for solving AX = K 273
9.3 Iterative methods for solving AX = K 282
9.4 Characteristic values and vectors 287
Answers to Selected Exercises 292
Appendix 309
Glossary of Mathematical Symbols 310
Index 313
|
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| dewey-search | 512.9/43 512/.5 |
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| discipline | Mathematik |
| edition | 2. ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:45:31Z |
| institution | BVB |
| isbn | 020101209X |
| language | English |
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| physical | XII, 318 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in mathematics |
| spelling | Cullen, Charles G. Verfasser aut Matrices and linear transformations 2. ed. Reading, MA u.a. Addison-Wesley 1972 XII, 318 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Matrices Transformations (Mathématiques) Transformations (Mathematics) Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004056740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cullen, Charles G. Matrices and linear transformations Matrices Transformations (Mathématiques) Transformations (Mathematics) Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4037968-1 |
| title | Matrices and linear transformations |
| title_auth | Matrices and linear transformations |
| title_exact_search | Matrices and linear transformations |
| title_full | Matrices and linear transformations |
| title_fullStr | Matrices and linear transformations |
| title_full_unstemmed | Matrices and linear transformations |
| title_short | Matrices and linear transformations |
| title_sort | matrices and linear transformations |
| topic | Matrices Transformations (Mathématiques) Transformations (Mathematics) Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Matrices Transformations (Mathématiques) Transformations (Mathematics) Matrix Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004056740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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