Elements of linear algebra and matrix theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
McGraw-Hill
1968
|
| Series: | International series in pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 370 S. |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804118059389026304 |
|---|---|
| adam_text | CONTENTS
Preface vii
1 Finite dimensional Vector Spaces 1
1.1 Vector Spaces 1
1.2 Directed Line Segments as Vectors 7
1.3 Geometric Vectors and Coordinate Spaces 16
1.4 Subspaces 24
1.5 Solutions of Linear Equations: Gauss Reduction 28
1.6 Solutions of Linear Equations: Determinants 35
1.7 Linear Dependence of Vectors 45
1.8 Basis and Dimension 51
1.9 Two Important Theorems 57
2 Linear Transformations and Matrices 63
2.1 Linear Transformations 63
2.2 Properties of Linear Transformations 69
2.3 Operations on Linear Transformations 73
2.4 Linear Functionals 79
2.5 Annihilators 85
2.6 Nonsingular Linear Transformations 90
2.7 Matrices of Linear Transformations 96
2.8 Matrices as Multiplicative Systems 106
2.9 Change of Basis 119
xi
xii CONTENTS
2.10 Rank 127
2.11 An Important Note of Clarification 134
3 Determinants and Systems of Linear Equations 140
3.1 Matrices and Linear Systems 140
3.2 Elementary Matrices and Inverses 146
3.3 Determinants as Multilinear Functionals 154
3.4 An Alternative Method for Evaluating a Determinant 160
3.5 An Introduction to Alternating Multilinear Forms 168
3.6 Determinants Discovered Anew 173
4 Inner product Spaces 178
4.1 Inner Products in F3 178
4.2 General Euclidean Space 186
4.3 The Gram Schmidt Process of Orthogonalization 193
4.4 Orthogonal Complements 199
4.5 Orthogonal Transformations 206
4.6 Linear Functionals and Adjoints 213
4.7 Inner Products and Positive Operators 221
4.8 Simple Applications of the Distance Function 229
5 Bilinear and Quadratic Forms 236
5.1 Bilinear Functions and Forms 236
5.2 Quadratic Forms 246
5.3 Diagonal Quadratic Forms under Congruence 252
5.4 Invariants of a Symmetric Matrix under Congruence 260
5.5 Eigenvalues and Eigenvectors 265
5.6 Orthogonal Reduction of Quadratic Forms 272
6 Similarity and Normal Operators 282
6.1 The Cayley Hamilton Theorem 282
6.2 Similarity and Diagonal Matrices 289
6.3 Complex Vector Spaces 297
6.4 The Spectral Theorem 305
6.5 Invariant Subspaces and Primary Decomposition 313
6.6 Nilpotent Operators and T cyclic Subspaces 321
6.7 The Jordan Canonical Form 327
Appendix 336
Selected Readings 340
Glossary of Symbols 341
Answers 342
Index 363
|
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| dewey-search | 512/.897 512.5 |
| dewey-sort | 3512 3897 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:16Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-91G DE-BY-TUM DE-11 DE-188 |
| physical | XII, 370 S. |
| psigel | HUB-ZB011201009 |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | International series in pure and applied mathematics |
| spelling | Moore, John Thomas Verfasser aut Elements of linear algebra and matrix theory John T. Moore New York [u.a.] McGraw-Hill 1968 XII, 370 S. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Algebras, Linear Matrices Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s DE-604 Lineare Algebra (DE-588)4035811-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moore, John Thomas Elements of linear algebra and matrix theory Algebras, Linear 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 | Elements of linear algebra and matrix theory |
| title_auth | Elements of linear algebra and matrix theory |
| title_exact_search | Elements of linear algebra and matrix theory |
| title_full | Elements of linear algebra and matrix theory John T. Moore |
| title_fullStr | Elements of linear algebra and matrix theory John T. Moore |
| title_full_unstemmed | Elements of linear algebra and matrix theory John T. Moore |
| title_short | Elements of linear algebra and matrix theory |
| title_sort | elements of linear algebra and matrix theory |
| topic | Algebras, Linear Matrices Matrix Mathematik (DE-588)4037968-1 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Matrices Matrix Mathematik Lineare Algebra |
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