Linear algebra and matrices:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
[2018]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 285 Seiten Illustrationen |
| ISBN: | 9781611975130 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804178277081808896 |
|---|---|
| adam_text | Contents
Preface ix
List of Symbols xi
1 Basic facts on vector spaces, matrices, and linear
transformations 1
1.1 Vector spaces............................................ 1
1.2 Dimension and basis...................................... 3
1.3 Matrices................................................. 13
1.4 Sum of subspaces.........................................24
1.5 Permutations.............................................30
1.6 Linear, multilinear maps and functions (first encounter) .... 34
1.7 Definition and properties of the determinant.............41
1.8 Permanents...............................................52
1.9 An application of the Philip Hall theorem................56
1.10 Polynomial rings.........................................61
1.11 The general linear group.................................67
1.12 Linear operators (second encounter)......................69
2 Canonical forms 75
2.1 Jordan canonical forms...................................75
2.2 An application of diagonalizable matrices................83
2.3 Matrix polynomials.......................................87
2.4 Minimal polynomial and decomposition to invariant subspaces 91
2.5 Quotient of vector spaces and induced linear operators .... 99
2.6 Isomorphism theorems for vector spaces...................100
2.7 Existence and uniqueness of the Jordan canonical form .... 102
2.8 Cyclic subspaces and rational canonical forms............108
Review Problems (1) 117
3 Applications of the Jordan canonical form 121
3.1 Functions of matrices ........................................121
3.2 Power stability, convergence, and boundedness of matrices . . 127
3.3 eAt and stability of certain systems of ordinary differential
equations.................................................. 132
4 Inner product spaces 139
4.1 Inner product............................................139
vii
Contents
viii
4.2 Explanation of the G-S process in standard Euclidean space 144
4.3 An example of the G-S process ...........................144
4.4 QR factorization.........................................144
4.5 An example of QR factorization...........................145
4.6 The best fit line........................................148
4.7 Geometric interpretation of the determinant (second encounter) 149
4.8 Special transformations in IPS...........................156
4.9 Symmetric bilinear, Hermitian, and quadratic forms.......161
4.10 Max-min characterizations of eigenvalues ................164
4.11 Positive definite operators and matrices ................173
4.12 Inequalities for traces .................................177
4.13 Singular value decomposition.............................181
4.14 Majorization.............................................185
4.15 Characterizations of singular values.....................190
4.16 Moore-Penrose generalized inverse .......................198
5 Perron—Frobenius theorem 207
5.1 Perron-Frobenius theorem.................................207
5.2 Irreducible matrices ....................................215
5.3 Recurrence equation with nonnegative coefficients........217
6 Tensor products 221
6.1 Introduction.............................................221
6.2 Tensor product of two vector spaces . ...................221
6.3 Tensor product of linear operators and the Kronecker product 224
6.4 Tensor product of many vector spaces ....................226
6.5 Examples and results for 3-tensors.......................229
Review Problems (2) 235
Challenging Problems 245
Appendices 247
A Sets and mappings 249
B Basic facts in analysis and topology 253
C Basic facts in graph theory 257
D Basic facts in abstract algebra 261
E Complex numbers 273
F Differential equations 277
G Basic notions of matrices 279
Bibliography 281
Index
283
|
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| id | DE-604.BV044758464 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:01:25Z |
| institution | BVB |
| isbn | 9781611975130 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030153933 |
| oclc_num | 1022847881 |
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| owner | DE-83 DE-739 DE-19 DE-BY-UBM |
| owner_facet | DE-83 DE-739 DE-19 DE-BY-UBM |
| physical | xv, 285 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Society for Industrial and Applied Mathematics |
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| spelling | Friedland, Shmuel 1944- (DE-588)113767021 aut Linear algebra and matrices Shmuel Friedland ; Mohsen Aliabadi, University of Illinois at Chicago, Chicago, Illinois Philadelphia Society for Industrial and Applied Mathematics [2018] © 2018 xv, 285 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Matrix Mathematik (DE-588)4037968-1 s DE-604 Aliabadi, Mohsen aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030153933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedland, Shmuel 1944- Aliabadi, Mohsen Linear algebra and matrices Matrix Mathematik (DE-588)4037968-1 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4035811-2 |
| title | Linear algebra and matrices |
| title_auth | Linear algebra and matrices |
| title_exact_search | Linear algebra and matrices |
| title_full | Linear algebra and matrices Shmuel Friedland ; Mohsen Aliabadi, University of Illinois at Chicago, Chicago, Illinois |
| title_fullStr | Linear algebra and matrices Shmuel Friedland ; Mohsen Aliabadi, University of Illinois at Chicago, Chicago, Illinois |
| title_full_unstemmed | Linear algebra and matrices Shmuel Friedland ; Mohsen Aliabadi, University of Illinois at Chicago, Chicago, Illinois |
| title_short | Linear algebra and matrices |
| title_sort | linear algebra and matrices |
| topic | Matrix Mathematik (DE-588)4037968-1 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Matrix Mathematik Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030153933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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