Schaum's outline of theory and problems of linear algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
2001
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Schaum's outline series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Nebentitel: Linear algebra |
| Beschreibung: | VIII, 424 S. |
| ISBN: | 0071362002 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128724911652864 |
|---|---|
| adam_text | SCHAUM S OUTLINE OF THEORY AND PROBLEMS OF LI N EAR ALGEBRA THIRD
EDITION ULB DARMSTADT III SEYMOUR LIPSCHUTZ, PH.D. TEMPLE UNIVERSITY
MARC LARS LIPSON, PH.D. UNIVERSITY OF GEORGIA SCHAUM S OUTLINE SERIES
MCGRAW-HILL NEW YORK CHICAGO SAN FRANCISCO LISBON LONDON MADRID MEXICO
CITY MILAN NEW DELHI SAN JUAN SEOUL SINGAPORE SYDNEY TORONTO CONTENTS
CHAPTER 1 VECTORS IN R N AND C , SPATIAL VECTORS 1.1 INTRODUCTION 1.2
VECTORS IN R 1.3 VECTOR ADDITION AND SCALAR MULTIPLICATION 1.4 DOT
(INNER) PRODUCT 1.5 LOCATED VECTORS, HYPERPLANES, LINES, CURVES IN R N
1.6 VECTORS IN R 3 (SPATIAL VECTORS), IJK NOTATION 1.7 COMPLEX NUMBERS
1.8 VECTORS IN C 1 2 3 4 7 10 12 14 CHAPTER 2 ALGEBRA OF MATRICES 2.1
INTRODUCTION 2.2 MATRICES 2.3 MATRIX ADDITION AND SCALAR MULTIPLICATION
2.4 SUMMATION SYMBOL 2.5 MATRIX MULTIPLICATION 2.6 TRANSPOSE OF A MATRIX
2.7 SQUARE MATRICES 2.8 POWERS OF MATRICES, POLYNOMIALS IN MATRICES 2.9
INVERTIBLE (NONSINGULAR) MATRICES 2.10 SPECIAL TYPES OF SQUARE MATRICES
2.11 COMPLEX MATRICES 2.12 BLOCK MATRICES 28 28 28 29 30 31 33 33 35 35
37 39 41 CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 59 3.1 INTRODUCTION 59
3.2 BASIC DEFINITIONS, SOLUTIONS 59 3.3 EQUIVALENT SYSTEMS, ELEMENTARY
OPERATIONS 62 3.4 SMALL SQUARE SYSTEMS OF LINEAR EQUATIONS 64 3.5
SYSTEMS IN TRIANGULAR AND ECHELON FORM 67 3.6 GAUSSIAN ELIMINATION 69
3.7 ECHELON MATRICES, ROW CANONICAL FORM, ROW EQUIVALENCE 73 3.8
GAUSSIAN ELIMINATION, MATRIX FORMULATION .76 3.9 MATRIX EQUATION OF A
SYSTEM OF LINEAR EQUATIONS 80 3.10 SYSTEMS OF LINEAR EQUATIONS AND
LINEAR COMBINATIONS OF VECTORS * 82 VI CONTENTS 3.11 HOMOGENEOUS SYSTEMS
OF LINEAR EQUATIONS 3.12 ELEMENTARY MATRICES 3.13 LU DECOMPOSITION 84 87
90 CHAPTER 4 VECTOR SPACES 4.1 INTRODUCTION 4.2 VECTOR SPACES 4.3
EXAMPLES OF VECTOR SPACES 4.4 LINEAR COMBINATIONS, SPANNING SETS 4.5
SUBSPACES 4.6 LINEAR SPANS, ROW SPACE OF A MATRIX 4.7 LINEAR DEPENDENCE
AND INDEPENDENCE 4.8 BASIS AND DIMENSION 4.9 APPLICATION TO MATRICES,
RANK OF A MATRIX 4.10 SUMS AND DIRECT SUMS 4.11 COORDINATES 116 116 116
117 119 121 123 126 129 131 134 135 CHAPTER 5 LINEAR MAPPINGS 171 5.1
INTRODUCTION 171 5.2 MAPPINGS, FUNCTIONS 171 5.3 LINEAR MAPPINGS (LINEAR
TRANSFORMATIONS) 174 5.4 KERNEL AND IMAGE OF A LINEAR MAPPING 176 5.5
SINGULAR AND NONSINGULAR LINEAR MAPPINGS, ISOMORPHISMS 180 5.6
OPERATIONS WITH LINEAR MAPPINGS 180 5.7 ALGEBRA A{ V) OF LINEAR
OPERATORS 181 CHAPTER 6 LINEAR MAPPINGS AND MATRICES 6.1 INTRODUCTION
6.2 MATRIX REPRESENTATION OF A LINEAR OPERATQR 6.3 CHANGE OF BASIS 6.4
SIMILARITY 6.5 MATRICES AND GENERAL LINEAR MAPPINGS 203 203 203 207 211
212 CHAPTER 7 INNER PRODUCT SPACES, ORTHOGONALITY 7.1 INTRODUCTION 7.2
INNER PRODUCT SPACES 7.3 EXAMPLES OF INNER PRODUCT SPACES 7.4
CAUCHY-SCHWARZ INEQUALITY, APPLICATIONS 7.5 ORTHOGONALITY 7.6 ORTHOGONAL
SETS AND BASES 7.7 GRAM-SCHMIDT ORTHOGONALIZATION PROCESS 7.8
ORTFIOGONAL AND POSITIVE DEFINITE MATRICES 7.9 COMPLEX INNER PRODUCT
SPACES 7.10 NORMED VECTOR SPACES (OPTIONAL) 236 236 236 237 240 241 243
246 247 249 251 CHAPTER 8 CHAPTER 9 CHAPTER 10 CHAPTER 11 CONTENTS
DETERMINANTS 8.1 INTRODUCTION 8.2 DETERMINANTS OF ORDER 1 AND 2 8.3
DETERMINANTS OF ORDER 3 8.4 PERMUTATIONS 8.5. DETERMINANTS OF ARBITRARY
ORDER 8.6 PROPERTIES OF DETERMINANTS 8.7 MINORS AND COFACTORS 8.8
EVALUATION OF DETERMINANTS 8.9 CLASSICAL ADJOINT 8.10 APPLICATIONS TO
LINEAR EQUATIONS, CRAMER S RULE 8.11 SUBMATRICES, MINORS, PRINCIPAL
MINORS 8.12 BLOCK MATRICES AND DETERMINANTS 8.13 DETERMINANTS AND VOLUME
8.14 DETERMINANT OF A LINEAR OPERATOR 8.15 MULTILINEARITY AND
DETERMINANTS DIAGONAIIZATION: EIGENVALUES AND EIGENVECTORS 9.1
INTRODUCTION 9.2 POLYNOMIALS OF MATRICES 9.3 CHARACTERISTIC POLYNOMIAL,
CAYLEY-HAMILTON THEOREM 9.4 DIAGONAIIZATION, EIGENVALUES AND
EIGENVECTORS 9.5 COMPUTING EIGENVALUES AND EIGENVECTORS, DIAGONALIZING
MATRICES 9.6 DIAGONALIZING REAL SYMMETRIC MATRICES 9.7 MINIMAL
POLYNOMIAL 9.8 CHARACTERISTIC AND MINIMAL POLYNOMIALS OF BLOCK MATRICES
CANONICAL FORMS 10.1 INTRODUCTION 10.2 TRIANGULAR FORM 10.3 INVARIANCE
10.4 INVARIANT DIRECT-SUM DECOMPOSITIONS 10.5 PRIMARY DECOMPOSITION 10.6
NILPOTENT OPERATORS 10.7 JORDAN CANONICAL FORM 10.8 CYCLIC SUBSPACES
10.9 RATIONAL CANONICAL FORM 10.10 QUOTIENT SPACES LINEAR FUNCTIONALS
AND THE DUAL SOACE VLL 277 277 277 278 280 281 282 283 284 285 285 286
287 288 288 289 306 306 307 308 310 314 315 317 319 340 340 340 341 342
343 343 344 345 345 346 365 11.1 INTRODUCTION 11.2 LINEAR FUNCTIONALS
AND THE DUAL SPACE 11.3 DUAL BASIS 365 365 366 VLLL CONTENTS 11.4 SECOND
DUAL SPACE 11.5 ANNIHILATORS 11.6 TRANSPOSE OF A LINEAR MAPPING 367 367
368 CHAPTER 12 BILINEAR, QUADRATIC, AND HERMITIAN FORMS 12.1
INTRODUCTION 12.2 BILINEAR FORMS 12.3 BILINEAR FORMS AND MATRICES 12.4
ALTERNATING BILINEAR FORMS 12.5 SYMMETRIC BILINEAR FORMS, QUADRATIC
FORMS 12.6 REAL SYMMETRIC BILINEAR FORMS, LAW OF INERTIA 12.7 HERMITIAN
FORMS 376 376 376 377 378 378 381 382 CHAPTER 13 LINEAR OPERATORS ON
INNER PRODUCT SPACES 395 13.1 INTRODUCTION 395 13.2 ADJOINT OPERATORS
395 13.3 ANALOGY BETWEEN A(V) AND C, SPECIAL LINEAR OPERATORS 397 13.4
SELF-ADJOINT OPERATORS 398 13.5 ORTHOGONAL AND UNITARY OPERATORS 398
13.6 ORTHOGONAL AND UNITARY MATRICES 399 13.7 CHANGE OF ORTHONORMAL
BASIS 400 13.8 POSITIVE DEFINITE AND POSITIVE OPERATORS 400 13.9
DIAGONAIIZATION AND CANONICAL FORMS IN INNER PRODUCT SPACES 401 13.10
SPECTRAL THEOREM 402 APPENDIX MULTILINEAR PRODUCTS A. 1 INTRODUCTION A.2
BILINEAR MAPPINGS AND TENSOR PRODUCTS A.3 ALTERNATING MULTILINEAR MAPS
AND EXTERIOR PRODUCTS 415 415 415 416 LIST OF SYMBOLS 420 INDEX 421
|
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| author | Lipschutz, Seymour Lipson, Marc |
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| ctrlnum | (OCoLC)248548249 (DE-599)BVBBV013886116 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| spelling | Lipschutz, Seymour Verfasser (DE-588)140841733 aut Schaum's outline of theory and problems of linear algebra Seymour Lipschutz ; Marc Lars Lipson Theory and problems of linear algebra Linear algebra 3. ed. New York [u.a.] McGraw-Hill 2001 VIII, 424 S. txt rdacontent n rdamedia nc rdacarrier Schaum's outline series Nebentitel: Linear algebra Lineare Algebra - Aufgabensammlung Lehrbuch (DE-588)4123623-3 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Lineare Algebra (DE-588)4035811-2 s Lehrbuch (DE-588)4123623-3 s 1\p DE-604 Lipson, Marc Verfasser (DE-588)123331730 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009499843&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lipschutz, Seymour Lipson, Marc Schaum's outline of theory and problems of linear algebra Lineare Algebra - Aufgabensammlung Lehrbuch (DE-588)4123623-3 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4123623-3 (DE-588)4035811-2 (DE-588)4143389-0 |
| title | Schaum's outline of theory and problems of linear algebra |
| title_alt | Theory and problems of linear algebra Linear algebra |
| title_auth | Schaum's outline of theory and problems of linear algebra |
| title_exact_search | Schaum's outline of theory and problems of linear algebra |
| title_full | Schaum's outline of theory and problems of linear algebra Seymour Lipschutz ; Marc Lars Lipson |
| title_fullStr | Schaum's outline of theory and problems of linear algebra Seymour Lipschutz ; Marc Lars Lipson |
| title_full_unstemmed | Schaum's outline of theory and problems of linear algebra Seymour Lipschutz ; Marc Lars Lipson |
| title_short | Schaum's outline of theory and problems of linear algebra |
| title_sort | schaum s outline of theory and problems of linear algebra |
| topic | Lineare Algebra - Aufgabensammlung Lehrbuch (DE-588)4123623-3 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra - Aufgabensammlung Lehrbuch Lineare Algebra Aufgabensammlung |
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