Matrix theory and linear algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Macmillan [u.a.]
1988
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 508 S. |
| ISBN: | 0023539518 |
Staff View
MARC
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| 245 | 1 | 0 | |a Matrix theory and linear algebra |c I. N. Herstein ; David J. Winter |
| 264 | 1 | |a New York |b Macmillan [u.a.] |c 1988 | |
| 300 | |a XVIII, 508 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Matrices | |
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Record in the Search Index
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| adam_text | Contents
Preface Y[[
List of Symbols xv xviii
1 The 2x2 Matrices 1
1.1 INTRODUCTION 1
1.2 DEFINITIONS AND OPERATIONS 2
1.3 SOME NOTATION 10
1.4 TRACE, TRANSPOSE, AND ODDS AND ENDS 15
1.5 DETERMINANTS 21
1.6 CRAMER S RULE 26
1.7 MAPPINGS 29
1.8 MATRICES AS MAPPINGS 35
1.9 THE CAYLEY HAMILTON THEOREM 38
1.10 COMPLEX NUMBERS 45
1.11 M2(C) 52
1.12 INNER PRODUCTS 55
2 Systems of Linear Equations 62
2.1 INTRODUCTION 62
2.2 EQUIVALENT SYSTEMS 74
2.3 ELEMENTARY ROW OPERATIONS. ECHELON MATRICES 79
2.4 SOLVING SYSTEMS OF LINEAR EQUATIONS 85
xi
3 The n x n Matrices 90
3.1 THE OPENING 90
3.2 MATRICES AS OPERATORS 98
3.3 TRACE 109
3.4 TRANSPOSE AND HERMITIAN ADJOINT 116
3.5 INNER PRODUCT SPACES 124
3.6 BASES OF Fin) 131
3.7 CHANGE OF BASIS OF f(n) 140
3.8 INVERTIBLE MATRICES 145
3.9 MATRICES AND BASES 148
3.10 BASES AND INNER PRODUCTS 157
4 More on n x n Matrices 164
4.1 SUBSPACES 164
4.2 MORE ON SUBSPACES 170
4.3 GRAM SCHMIDT ORTHOGONALIZATION PROCESS 176
4.4 RANK AND NULLITY 180
4.5 CHARACTERISTIC ROOTS 183
4.6 HERMITIAN MATRICES 192
4.7 TRIANGULARIZING MATRICES WITH COMPLEX ENTRIES 199
4.8 TRIANGULARIZING MATRICES WITH REAL
ENTRIES (OPTIONAL) 208
5 Determinants 214
5.1 INTRODUCTION 214
5.2 PROPERTIES OF DETERMINANTS: ROW OPERATIONS 221
5.3 PROPERTIES OF DETERMINANTS: COLUMN OPERATIONS 233
5.4 CRAMER S RULE 243
5.5 PROPERTIES OF DETERMINANTS: OTHER EXPANSIONS 246
5.6 THE CLASSICAL ADJOINT (OPTIONAL) 253
5.7 ELEMENTARY MATRICES 256
5.8 THE DETERMINANT OF THE PRODUCT 262
5.9 THE CHARACTERISTIC POLYNOMIAL 266
5.10 THE CAYLEY HAMILTON THEOREM 270
6 Rectangular Matrices.
More on Determinants 273
6.1 RECTANGULAR MATRICES 273
6.2 BLOCK MULTIPLICATION (OPTIONAL) 275
6.3 ELEMENTARY BLOCK MATRICES (OPTIONAL) 278
6.4 A CHARACTERIZATION OF THE DETERMINANT
FUNCTION (OPTIONAL) 280
7 More on Systems of Linear Equations 282
7.1 LINEAR TRANSFORMATIONS FROM f 1 to F[m) 282
7.2 THE NULLSPACE AND COLUMN SPACE OF AN m x n
MATRIX 287
8 Abstract Vector Spaces 292
8.1 INTRODUCTION, DEFINITIONS, AND EXAMPLES 292
8.2 SUBSPACES 296
8.3 HOMOMORPHISMS AND ISOMORPHISMS 300
8.4 ISOMORPHISMS FROM V TO FM 307
8.5 LINEAR INDEPENDENCE IN INFINITE DIMENSIONAL VECTOR
SPACES 311
8.6 INNER PRODUCT SPACES 314
8.7 MORE ON INNER PRODUCT SPACES 321
9 Linear Transformations 330
9.1 INTRODUCTION 330
9.2 DEFINITIONS, EXAMPLES, AND SOME PRELIMINARY
RESULTS 331
9.3 PRODUCTS OF LINEAR TRANSFORMATIONS 337
9.4 LINEAR TRANSFORMATIONS AS MATRICES 342
9.5 A DIFFERENT SLANT ON SECTION 9.4 (OPTIONAL) 349
9.6 HERMITIAN IDEAS 351
9.7 QUOTIENT SPACES (OPTIONAL) 357
9.8 INVARIANT SUBSPACES (OPTIONAL) 366
9.9 LINEAR TRANSFORMATIONS FROM ONE SPACE TO
ANOTHER 372
10 The Jordan Canonical Form (Optional) 376
10.1 INTRODUCTION 376
10.2 GENERALIZED NULLSPACES 380
10.3 THE JORDAN CANONICAL FORM 386
10.4 EXPONENTIALS 393
10.5 SOLVING HOMOGENEOUS SYSTEMS OF LINEAR DIFFERENTIAL
EQUATIONS 400
11 Applications (Optional) 408
11.1 FIBONACCI NUMBERS 408
11.2 EQUATIONS OF CURVES 414
11.3 MARKOV PROCESSES 416
11.4 INCIDENCE MODELS 423
11.5 DIFFERENTIAL EQUATIONS 430
12 Least Squares Methods (Optional) 434
12.1 APPROXIMATE SOLUTIONS OF SYSTEMS OF LINEAR
EQUATIONS 434
12.2 THE APPROXIMATE INVERSE OF AN m x n MATRIX 443
12.3 SOLVING A MATRIX EQUATION USING ITS NORMAL
EQUATION 446
12.4 FINDING FUNCTIONS THAT APPROXIMATE DATA 450
12.5 WEIGHTED APPROXIMATION 455
13 Linear Algorithms (Optional) 458
13.1 INTRODUCTION 458
13.2 THE LDU FACTORIZATION OF A 461
13.3 THE ROW REDUCTION ALGORITHM AND ITS INVERSE 467
13.4 BACK AND FORWARD SUBSTITUTION. SOLVING Ax = y 476
13.5 APPROXIMATE INVERSE AND PROJECTION ALGORITHMS 482
13.6 A COMPUTER PROGRAM FOR FINDING EXACT AND
APPROXIMATE SOLUTIONS 488
Index 501
|
| any_adam_object | 1 |
| author | Herstein, Israel Nathan 1923-1988 Winter, David J. |
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| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004623261 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:15:07Z |
| institution | BVB |
| isbn | 0023539518 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002840111 |
| oclc_num | 15695741 |
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| owner_facet | DE-384 DE-739 DE-83 DE-706 DE-188 |
| physical | XVIII, 508 S. |
| psigel | TUB-www |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Macmillan [u.a.] |
| record_format | marc |
| spelling | Herstein, Israel Nathan 1923-1988 Verfasser (DE-588)1047675560 aut Matrix theory and linear algebra I. N. Herstein ; David J. Winter New York Macmillan [u.a.] 1988 XVIII, 508 S. txt rdacontent n rdamedia nc rdacarrier Algebras, Linear Matrices Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Matrizenrechnung (DE-588)4126963-9 s Winter, David J. Verfasser (DE-588)120601613 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002840111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Herstein, Israel Nathan 1923-1988 Winter, David J. Matrix theory and linear algebra Algebras, Linear Matrices Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4035811-2 |
| title | Matrix theory and linear algebra |
| title_auth | Matrix theory and linear algebra |
| title_exact_search | Matrix theory and linear algebra |
| title_full | Matrix theory and linear algebra I. N. Herstein ; David J. Winter |
| title_fullStr | Matrix theory and linear algebra I. N. Herstein ; David J. Winter |
| title_full_unstemmed | Matrix theory and linear algebra I. N. Herstein ; David J. Winter |
| title_short | Matrix theory and linear algebra |
| title_sort | matrix theory and linear algebra |
| topic | Algebras, Linear Matrices Matrizenrechnung (DE-588)4126963-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Matrices Matrizenrechnung Lineare Algebra |
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