Linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Mineola, NY
Dover Publications
2014
|
| Ausgabe: | Dover edition |
| Schlagworte: | |
| Online-Zugang: | Publisher description Contributor biographical information Inhaltsverzeichnis |
| Beschreibung: | Originally published: Oxford : Oxford University Press, 1992. - Includes indexes |
| Beschreibung: | xiv, 358 pages 24 cm |
| ISBN: | 9780486780559 0486780554 |
Internformat
MARC
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| 245 | 1 | 0 | |a Linear algebra |c Sterling K. Berberian, Prof. Emer., Mathematics, The University of Texas at Austin |
| 250 | |a Dover edition | ||
| 264 | 1 | |a Mineola, NY |b Dover Publications |c 2014 | |
| 300 | |a xiv, 358 pages |c 24 cm | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Algebras, Linear | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PART I I Vector spaces 3
1.1 Motivation (vectors in 3-space) 3
1.2 Rn and Cn 8
1.3 Vector spaces: the axioms, some examples 10
1.4 Vector spaces: first consequences of the axioms 14
1.5 Linear combinations of vectors 17
1.6 Linear subspaces 19
2 Linear mappings 25
2.1 Linear mappings 25
2.2 Linear mappings and linear subspaces:
kernel and range 29
2.3 Spaces of linear mappings: J?(V, W) and J2(V) 32
2.4 Isomorphic vector spaces 37
2.5 Equivalence relations and quotient sets 40
2.6 Quotient vector spaces 46
2.7 The first isomorphism theorem 49
3 Structure of vector spaces 52
3.1 Linear subspace generated by a subset 53
3.2 Linear dependence 55
3.3 Linear independence 58
3.4 Finitely generated vector spaces 63
3.5 Basis, dimension 65
3.6 Rank + nullity = dimension 74
3.7 Applications of R + N = D 77
3.8 Dimension of Jt(V, W) 81
3.9 Duality in vector spaces 85
xii
CONTENTS
4 Matrices 92
4.1 Matrices 92
4.2 Matrices of linear mappings 96
4.3 Matrix multiplication 102
4.4 Algebra of matrices 105
4.5 A model for linear mappings 108
4.6 Transpose of a matrix 110
4.7 Calculating the rank 114
4.8 When is a linear system solvable? 120
4.9 An example 122
4.10 Change of basis, similar matrices 125
5 Inner product spaces 131
5.1 Inner product spaces, Euclidean spaces 131
5.2 Duality in inner product spaces 136
5.3 The adjoint of a linear mapping 143
5.4 Orthogonal mappings and matrices 147
6 Determinants (2x2 and 3x3) 154
6.1 Determinant of a 2 x 2 matrix 155
6.2 Cross product of vectors in R3 158
6.3 Determinant of a 3 x 3 matrix 162
6.4 Characteristic polynomial of a matrix (2 x 2 or 3 x 3) 165
6.5 Diagonalizing 2x2 symmetric real matrices 173
6.6 Diagonalizing 3x3 symmetric real matrices 177
6.7 A geometric application (conic sections) 182
PART II 7 Determinants (nx n) 193
7.1 Alternate multilinear forms 193
7.2 Determinant of a linear mapping 199
7.3 Determinant of a square matrix 202
7.4 Cofactors 205
8 Similarity (Act I) 212
8.1 Similarity 212
CONTENTS
xili
8.2 Eigenvalues and eigenvectors 2!5
8.3 Characteristic polynomial 218
9 Euclidean spaces (Spectral Theory) 226
9.1 Invariant and reducing subspaces 226
9.2 Bounds of a linear mapping 231
9.3 Bounds of a self-adjoint mapping, Spectral Theorem 235
9.4 Normal linear mappings in Euclidean spaces 238
10 Equivalence of matrices over a PIR 244
10.1 Unimodular matrices 244
10.2 Preview of the theory of equivalence 246
10.3 Equivalence: existence of a diagonal form 248
10.4 Equivalence: uniqueness of the diagonal form 255
11 Similarity (Act II) 261
I l.l Invariant factors, Fundamental theorem of similarity 261
11.2 Companion matrix, Rational canonical form 269
11.3 Hamilton-Cayley theorem, minimal polynomial 273
11.4 Elementary divisors, Jordan canonical form 279
11.5 Appendix: proof that Mn(F)[i] = Mn(F[i]) 284
12 Unitary spaces 286
12.1 Complex inner product spaces, unitary spaces 286
12.2 Orthogonality 290
12.3 Orthonormal bases, isomorphism 292
12.4 Adjoint of a linear mapping 294
12.5 Invariant and reducing subspaces 298
12.6 Special linear mappings and matrices 299
12.7 Normal linear mappings, Spectral Theorem 301
12.8 The Spectral Theorem: another way 301
13 Tensor products 317
13.1 Tensor product V 8 W of vector spaces 317
13.2 Tensor product S® Tof linear mappings 318
13.3 Matrices of tensor products 322
xiv
CONTENTS
Appendix A Foundations 326
A. I A dab of logic 326
A.2 Set notations 332
A.3 Functions 335
A. 4 The axioms for a field 337
Appendix B Integral domains, factorization
theory 338
B. l The field of fractions of an integral domain 338
B.2 Divisibility in an integral domain 340
B.3 Principal ideal rings 343
B.4 Euclidean integral domains 346
B.5 Factorization in overfields 347
Appendix C Weierstrass-Bolzano theorem 350
Index of notations 353
Index 355
Errata and Comments 357
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.5 |
| dewey-sort | 3512 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Dover edition |
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| id | DE-604.BV043814659 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:35:48Z |
| institution | BVB |
| isbn | 9780486780559 0486780554 |
| language | English |
| lccn | 014010527 |
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| physical | xiv, 358 pages 24 cm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Dover Publications |
| record_format | marc |
| spelling | Berberian, Sterling K. 1926- Verfasser (DE-588)171973232 aut Linear algebra Sterling K. Berberian, Prof. Emer., Mathematics, The University of Texas at Austin Dover edition Mineola, NY Dover Publications 2014 xiv, 358 pages 24 cm txt rdacontent n rdamedia nc rdacarrier Originally published: Oxford : Oxford University Press, 1992. - Includes indexes Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 http://www.loc.gov/catdir/enhancements/fy1408/2014010527-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy1408/2014010527-b.html Contributor biographical information 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=029225816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berberian, Sterling K. 1926- Linear algebra Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Linear algebra |
| title_auth | Linear algebra |
| title_exact_search | Linear algebra |
| title_full | Linear algebra Sterling K. Berberian, Prof. Emer., Mathematics, The University of Texas at Austin |
| title_fullStr | Linear algebra Sterling K. Berberian, Prof. Emer., Mathematics, The University of Texas at Austin |
| title_full_unstemmed | Linear algebra Sterling K. Berberian, Prof. Emer., Mathematics, The University of Texas at Austin |
| title_short | Linear algebra |
| title_sort | linear algebra |
| topic | Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Lineare Algebra |
| url | http://www.loc.gov/catdir/enhancements/fy1408/2014010527-d.html http://www.loc.gov/catdir/enhancements/fy1408/2014010527-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029225816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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