Verfügbarkeit: Linear algebra and matrices | Technische Universität München

Linear algebra and matrices:

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Bibliographische Detailangaben
Beteiligte Personen:	Friedland, Shmuel 1944- (VerfasserIn), Aliabadi, Mohsen (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Philadelphia Society for Industrial and Applied Mathematics [2018]
Schlagwörter:	Matrix > Mathematik Lineare Algebra
Links:	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
Umfang:	xv, 285 Seiten Illustrationen
ISBN:	9781611975130

Internformat

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Datensatz im Suchindex

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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	2024-12-20T18:10:54Z
institution	BVB
isbn	9781611975130
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-030153933
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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
record_format	marc
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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