Applied linear algebra: the decoupling principle
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2008
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 371 S. graph. Darst. |
| ISBN: | 9780821844410 9781470470043 0821844415 |
Internformat
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| 245 | 1 | 0 | |a Applied linear algebra |b the decoupling principle |c Lorenzo Sadun |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2008 | |
| 300 | |a XVIII, 371 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1821327533385187328 |
|---|---|
| adam_text |
APPLIED LINEAR ALGEBRA THE DECOUPLING PRINCIPLE SECOND EDITION LORENZO
SADUN »AMS AMERICAN MATHEMATICAL SOCIETY CONTENTS PREFACE TO SECOND
EDITION IX PREFACE XI CHAPTER 1. THE DECOUPLING PRINCIPLE 1 EXPLORATION:
BEATS 8 CHAPTER 2. VECTOR SPACES AND BASES 9 §2.1. VECTOR SPACES 9 §2.2.
LINEAR INDEPENDENCE, BASIS, AND DIMENSION 14 §2.3. PROPERTIES AND USES
OF A BASIS 21 EXPLORATION: POLYNOMIALS 24 §2.4. CHANGE OF BASIS - 25
§2.5. BUILDING NEW VECTOR .SPACES FROM OLD ONES. 29 EXPLORATION:
PROJECTIONS - ' 35 CHAPTER 3. LINEAR TRANSFORMATIONS AND OPERATORS 37
§3.1. DEFINITIONS AND EXAMPLES 37 EXPLORATION: COMPUTER GRAPHICS 43
§3.2. THE MATRIX OF A LINEAR TRANSFORMATION 44 §3.3. THE EFFECT OF A
CHANGE OF BASIS 48 §3.4. INFINITE DIMENSIONAL VECTOR SPACES 51 §3.5.
KERNELS, RANGES, AND QUOTIENT MAPS 53 VI CONTENTS CHAPTER 4. AN
INTRODUCTION TO EIGENVALUES 57 §4.1. DEFINITIONS AND EXAMPLES 57 §4.2.
BASES OF EIGENVECTORS 59 §4.3. EIGENVALUES AND THE CHARACTERISTIC
POLYNOMIAL 61 §4.4. THE NEED FOR COMPLEX EIGENVALUES 67 EXPLORATION:
CIRCLES AND ELLIPSES 71 §4.5. WHEN IS AN OPERATOR DIAGONALIZABLE? 72
§4.6. TRACES, DETERMINANTS, AND TRICKS OF THE TRADE 77 §4.7.
SIMULTANEOUS DIAGONALIZATION OF TWO OPERATORS 82 §4.8. EXPONENTIALS OF
COMPLEX NUMBERS AND MATRICES 86 §4.9. POWER VECTORS AND JORDAN CANONICAL
FORM 90 CHAPTER 5. SOME CRUCIAL APPLICATIONS 97 §5.1. DISCRETE-TIME
EVOLUTION: X(N) = AX(N * 1) 97 EXPLORATION: FIBONACCI NUMBERS AND
TILINGS 103 §5.2. FIRST-ORDER CONTINUOUS-TIME EVOLUTION: DX/DT = AX 104
§5.3. SECOND-ORDER CONTINUOUS-TIME EVOLUTION: D 2 X/DT 2 * AX 108 §5.4.
REDUCING SECOND-ORDER PROBLEMS TO FIRST-ORDER 116 EXPLORATION:
DIFFERENCE EQUATIONS 119 §5.5. LONG-TIME BEHAVIOR AND STABILITY 120
§5.6. MARKOV CHAINS AND PROBABILITY MATRICES 126 EXPLORATION: RANDOM
WALKS 135 §5.7. LINEAR ANALYSIS NEAR FIXED POINTS OF NONLINEAR PROBLEMS
136 EXPLORATION: NONLINEAR ODES, "-" 143 CHAPTER 6. INNER PRODUCTS 145
§6.1. REAL INNER PRODUCTS: DEFINITIONS AND EXAMPLES 145 §6.2. COMPLEX
INNER PRODUCTS 149 §6.3. BRAS, KETS, AND DUALITY 152 §6.4. EXPANSION IN
ORTHONORMAL BASES: FINDING COEFFICIENTS 158 §6.5. PROJECTIONS AND THE
GRAM-SCHMIDT PROCESS 161 §6.6. ORTHOGONAL COMPLEMENTS AND PROJECTIONS
ONTO SUBSPACES 167 §6.7. LEAST SQUARES SOLUTIONS 170 EXPLORATION: CURVE
FITTING 176 §6.8. THE SPACES 2 AND L 2 177 §6.9. FOURIER SERIES ON AN
INTERVAL 182 CONTENTS VII EXPLORATION: FOURIER SERIES 188 CHAPTER 7.
ADJOINTS, HERMITIAN OPERATORS, AND UNITARY OPERATORS 189 §7.1. ADJOINTS
AND TRANSPOSES 190 §7.2. HERMITIAN OPERATORS 194 §7.3. QUADRATIC FORMS
AND REAL SYMMETRIC MATRICES 200 §7.4. ROTATIONS, ORTHOGONAL OPERATORS,
AND UNITARY OPERATORS 207 EXPLORATION: NORMAL MATRICES 215 §7.5. HOW THE
FOUR CLASSES ARE RELATED 216 EXPLORATION: REPRESENTATIONS OF SU2 220
CHAPTER 8. THE WAVE EQUATION 223 §8.1. WAVES ON THE LINE 224 §8.2. WAVES
ON THE HALF-LINE: DIRICHLET AND NEUMANN BOUNDARY CONDITIONS 227 §8.3.
THE VIBRATING STRING 232 EXPLORATION: DISCRETIZING THE WAVE EQUATION 235
§8.4. STANDING WAVES AND FOURIER SERIES 237 §8.5. PERIODIC BOUNDARY
CONDITIONS 242 §8.6. EQUIVALENCE OF TRAVELING WAVES AND STANDING WAVES
250 §8.7. THE DIFFERENT TYPES OF FOURIER SERIES 254 CHAPTER 9.
CONTINUOUS SPECTRA AND THE DIRAC DELTA FUNCTION 259 §9.1. THE SPECTRUM
OF A LINEAR OPERATOR 260 §9.2. THE DIRAC 5 FUNCTION 264 §9.3.
DISTRIBUTIONS - *' . / 269 §9.4. GENERALIZED EIGENFUNCTION EXPANSIONS:
THE SPECTRAL THEOREM 272 CHAPTER 10. FOURIER TRANSFORMS 281 §10.1.
EXISTENCE OF FOURIER TRANSFORMS 281 §10.2. BASIC PROPERTIES OF FOURIER
TRANSFORMS 286 §10.3. CONVOLUTIONS AND DIFFERENTIAL EQUATIONS 292
EXPLORATION: THE CENTRAL LIMIT THEOREM 294 §10.4. PARTIAL DIFFERENTIAL
EQUATIONS 295 §10.5. BANDWIDTH AND HEISENBERG'S UNCERTAINTY PRINCIPLE
301 §10.6. FOURIER TRANSFORMS ON THE HALF-LINE 306 VIII CHAPTER 11.
GREEN'S FUNCTIONS §11.1. DELTA FUNCTIONS AND THE SUPERPOSITION PRINCIPLE
§11.2. INVERTING OPERATORS §11.3. THE METHOD OF IMAGES §11.4. INITIAL
VALUE PROBLEMS §11.5. LAPLACE'S EQUATION ON M 2 APPENDIX A. MATRIX
OPERATIONS §A.L. MATRIX MULTIPLICATION §A.2. ROW REDUCTION §A.3. RANK
§A.4. SOLVING AX = 0. §A.5. THE COLUMN SPACE §A.6. SUMMARY APPENDIX B.
SOLUTIONS TO SELECTED EXERCISES INDEX CONTENTS 311 311 314 319 325 330
337 337 338 340 341 342 343 345 369 |
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| author | Sadun, Lorenzo Adlai |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)180190950 (DE-599)BSZ277737222 |
| 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 | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-01-15T15:01:30Z |
| institution | BVB |
| isbn | 9780821844410 9781470470043 0821844415 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019003807 |
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| owner_facet | DE-523 DE-83 DE-188 DE-91G DE-BY-TUM |
| physical | XVIII, 371 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | American Mathematical Society |
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| spelling | Sadun, Lorenzo Adlai Verfasser aut Applied linear algebra the decoupling principle Lorenzo Sadun 2. ed. Providence, RI American Mathematical Society 2008 XVIII, 371 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019003807&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sadun, Lorenzo Adlai Applied linear algebra the decoupling principle Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Applied linear algebra the decoupling principle |
| title_auth | Applied linear algebra the decoupling principle |
| title_exact_search | Applied linear algebra the decoupling principle |
| title_full | Applied linear algebra the decoupling principle Lorenzo Sadun |
| title_fullStr | Applied linear algebra the decoupling principle Lorenzo Sadun |
| title_full_unstemmed | Applied linear algebra the decoupling principle Lorenzo Sadun |
| title_short | Applied linear algebra |
| title_sort | applied linear algebra the decoupling principle |
| title_sub | the decoupling principle |
| topic | Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019003807&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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