Linear algebra and its applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, N.J.
Wiley-Interscience
2007
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/toc/ecip0719/2007023226.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275059&sequence=000008&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Frühere Aufl. u.d.T.: Linear algebra |
| Umfang: | XV, 376 S. |
| ISBN: | 0471751561 9780471751564 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV023071919 | ||
| 003 | DE-604 | ||
| 005 | 20230223 | ||
| 007 | t| | ||
| 008 | 080109s2007 xxu |||| 00||| eng d | ||
| 010 | |a 2007023226 | ||
| 020 | |a 0471751561 |c cloth |9 0-471-75156-1 | ||
| 020 | |a 9780471751564 |9 978-0-471-75156-4 | ||
| 035 | |a (OCoLC)138342469 | ||
| 035 | |a (DE-599)BVBBV023071919 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 |a DE-29T |a DE-91G |a DE-634 |a DE-20 |a DE-521 | ||
| 050 | 0 | |a QA184.2 | |
| 082 | 0 | |a 512/.5 | |
| 084 | |a SK 220 |0 (DE-625)143224: |2 rvk | ||
| 084 | |a MAT 150f |2 stub | ||
| 100 | 1 | |a Lax, Peter D. |d 1926- |e Verfasser |0 (DE-588)130442437 |4 aut | |
| 245 | 1 | 0 | |a Linear algebra and its applications |c Peter D. Lax |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, N.J. |b Wiley-Interscience |c 2007 | |
| 300 | |a XV, 376 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 500 | |a Frühere Aufl. u.d.T.: Linear algebra | ||
| 650 | 7 | |a Álgebra linear |2 larpcal | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip0719/2007023226.html |3 Inhaltsverzeichnis | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275059&sequence=000008&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016275059 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 150f 2005 A 1924(2) 0202 MAT 150f 2009 A 498(2) |
|---|---|
| DE-BY-TUM_katkey | 1656773 |
| DE-BY-TUM_location | 01 02 |
| DE-BY-TUM_media_number | 040010200578 040010200603 040020778861 |
| _version_ | 1821933428872839168 |
| adam_text | Contents
Preface xi
Preface to the First Edition xiii
1. Fundamentals 1
Linear Space, Isomorphism 1
Subspace 4
Linear Dependence 4
Basis, Dimension 5
Quotient Space 8
2. Duality 13
Linear Functions 13
Dual of a Linear Space 14
Annihilator 15
Codimension 16
Quadrature Formula 17
3. Linear Mappings 19
Domain and Target Space 19
Nullspace and Range 20
Fundamental Theorem 20
Underdetermined Linear Systems 21
Interpolation 22
Difference Equations 23
Algebra of Linear Mappings 24
Dimension of Nullspace and Range 27
Transposition 26
Similarity 29
Projections 30
4. Matrices 32
Rows and Columns 33
Matrix Multiplication 35
v
Vi CONTENTS
Transposition 36
Rank 37
Gaussian Elimination 39
5. Determinant and Trace 44
Ordered Simplices 44
Signed Volume, Determinant 45
Permutation Group 46
Formula for Determinant 48
Multiplicative Property 49
Laplace Expansion 52
Cramer s Rule 54
Trace 55
6. Spectral Theory 58
Iteration of Linear Maps 59
Eigenvalues, Eigenvectors 59
Fibonacci Sequence 62
Characteristic Polynomial 63
Trace and Determinant Revisited 65
Spectral Mapping Theorem 66
Cayley-Hamilton Theorem 67
Generalized Eigenvectors 69
Spectral Theorem 70
Minimal Polynomial 72
When Are Two Matrices Similar 73
Commuting Maps 74
7. Euclidean Structure 77
Scalar Product, Distance 79
Schwarg Inequality 79
Orthonormal Basis 80
Gram-Schmidt 81
Orthogonal Complement 82
Orthogonal Projection 83
Adjoint 84
Overdetermined Systems 86
Isometry 87
The Orthogonal Group 89
Norm of a Linear Map 89
Completeness Local Compactness 92
Complex Euclidean Structure 95
Spectral Radius 97
Hilbert-Schmidt Norm 98
Cross Product 99
CONTENTS Vii
8. Spectral Theory of Self-Adjoint Mappings 101
Quadratic Forms 102
Law of Inertia 103
Spectral Resolution 105
Commuting Maps 111
Anti-Self-Adjoint Maps 112
Normal Maps 112
Rayleigh Quotient 114
Minmax Principle 116
Norm and Eigenvalues 119
9. Calculus of Vector- and Matrix-Valued Functions 121
Convergence in Norm 121
Rules of Differentiation 122
Derivative of det A(t) 126
Matrix Exponential 128
Simple Eigenvalues 129
Multiple Eigenvalues 135
Rellich s Theorem 140
Avoidance of Crossing 140
10. Matrix Inequalities 143
Positive Self-Adjoint Matrices 143
Monotone Matrix Functions 151
Gram Matrices 152
Schur s Theorem 153
The Determinant of Positive Matrices 154
Integral Formula for Determinants 157
Eigenvalues 160
Separation of Eigenvalues 161
Wielandt-Hoffman Theorem 164
Smallest and Largest Eigenvalue 166
Matrices with Positive Self-Adjoint Part 167
Polar Decomposition 169
Singular Values 170
Singular Value Decomposition 170
11. Kinematics and Dynamics 172
Axis and Angle of Rotation 172
Rigid Motion 173
Angular Velocity Vector 176
Fluid Flow 177
Curl and Divergence 179
Small Vibrations 180
Conservation of Energy 182
Frequencies and Normal Modes 184
Viii CONTENTS
12. Convexity 187
Convex Sets 187
Gauge Function 188
Hahn-Banach Theorem 191
Support Function 193
Caratheodory s Theorem 195
Konig-Birkhoff Theorem 198
Helly s Theorem 199
13. The Duality Theorem 202
Farkas-Minkowski Theorem 203
Duality Theorem 206
Economics Interpretation 208
Minmax Theorem 210
14. Normed Linear Spaces 214
Norm 214
F Norms 215
Equivalence of Norms 217
Completeness 219
Local Compactness 219
Theorem of F. Riesz 219
Dual Norm 222
Distance from Subspace 223
Normed Quotient Space 224
Complex Normed Spaces 226
Complex Hahn-Banach Theorem 226
Characterization of Euclidean Spaces 227
15. Linear Mappings Between Normed Linear Spaces 229
Norm of a Mapping 230
Norm of Transpose 231
Normed Algebra of Maps 232
Invertible Maps 233
Spectral Radius 236
16. Positive Matrices 237
Perron s Theorem 237
Stochastic Matrices 240
Frobenius Theorem 243
17. How to Solve Systems of Linear Equations 246
History 246
Condition Number 248
Iterative Methods 248
Steepest Descent 249
Chebychev Iteration 252
CONTENTS ix
Three-term Chebychev Iteration 255
Optimal Three-Term Recursion Relation 256
Rate of Convergence 261
18. How to Calculate the Eigenvalues of Self-Adjoint Matrices 262
QR Factorization 262
Using the QR Factorization to Solve Systems of Equations 263
The QR Algorithm for Finding Eigenvalues 263
Householder Reflection for QR Factorization 266
Tridiagonal Form 267
Analogy of QR Algorithm and Toda Flow 269
Moser s Theorem 273
More General Flows 276
19. Solutions 278
Bibliography 300
Appendix 1. Special Determinants 302
Appendix 2. The Pfaffian 305
Appendix 3. Symplectic Matrices 308
Appendix 4. Tensor Product 313
Appendix 5. Lattices 317
Appendix 6. Fast Matrix Multiplication 320
Appendix 7. Gershgorin s Theorem 323
Appendix 8. The Multiplicity of Eigenvalues 325
Appendix 9. The Fast Fourier Transform 328
Appendix 10. The Spectral Radius 334
Appendix 11. The Lorentz Group 342
Appendix 12. Compactness of the Unit Ball 352
Appendix 13. A Characterization of Commutators 355
Appendix 14. Liapunov s Theorem 357
Appendix 15. The Jordan Canonical Form 363
Appendix 16. Numerical Range 367
Index 373
|
| any_adam_object | 1 |
| author | Lax, Peter D. 1926- |
| author_GND | (DE-588)130442437 |
| author_facet | Lax, Peter D. 1926- |
| author_role | aut |
| author_sort | Lax, Peter D. 1926- |
| author_variant | p d l pd pdl |
| building | Verbundindex |
| bvnumber | BV023071919 |
| callnumber-first | Q - Science |
| callnumber-label | QA184 |
| callnumber-raw | QA184.2 |
| callnumber-search | QA184.2 |
| callnumber-sort | QA 3184.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)138342469 (DE-599)BVBBV023071919 |
| 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 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01666nam a2200457zc 4500</leader><controlfield tag="001">BV023071919</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230223 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">080109s2007 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2007023226</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0471751561</subfield><subfield code="c">cloth</subfield><subfield code="9">0-471-75156-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780471751564</subfield><subfield code="9">978-0-471-75156-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)138342469</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023071919</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-521</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA184.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.5</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 220</subfield><subfield code="0">(DE-625)143224:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 150f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lax, Peter D.</subfield><subfield code="d">1926-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)130442437</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linear algebra and its applications</subfield><subfield code="c">Peter D. Lax</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, N.J.</subfield><subfield code="b">Wiley-Interscience</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 376 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Pure and applied mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Frühere Aufl. u.d.T.: Linear algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Álgebra linear</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebras, Linear</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare Algebra</subfield><subfield code="0">(DE-588)4035811-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare Algebra</subfield><subfield code="0">(DE-588)4035811-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/toc/ecip0719/2007023226.html</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275059&sequence=000008&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016275059</subfield></datafield></record></collection> |
| id | DE-604.BV023071919 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:07:59Z |
| institution | BVB |
| isbn | 0471751561 9780471751564 |
| language | English |
| lccn | 2007023226 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016275059 |
| oclc_num | 138342469 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-91G DE-BY-TUM DE-634 DE-20 DE-521 |
| owner_facet | DE-703 DE-29T DE-91G DE-BY-TUM DE-634 DE-20 DE-521 |
| physical | XV, 376 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Wiley-Interscience |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spellingShingle | Lax, Peter D. 1926- Linear algebra and its applications Álgebra linear larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Linear algebra and its applications |
| title_auth | Linear algebra and its applications |
| title_exact_search | Linear algebra and its applications |
| title_full | Linear algebra and its applications Peter D. Lax |
| title_fullStr | Linear algebra and its applications Peter D. Lax |
| title_full_unstemmed | Linear algebra and its applications Peter D. Lax |
| title_short | Linear algebra and its applications |
| title_sort | linear algebra and its applications |
| topic | Álgebra linear larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Álgebra linear Algebras, Linear Lineare Algebra |
| url | http://www.loc.gov/catdir/toc/ecip0719/2007023226.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275059&sequence=000008&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT laxpeterd linearalgebraanditsapplications |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 150f 2005 A 1924(2) Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |
Teilbibliothek Physik
| Signatur: |
0202 MAT 150f 2009 A 498(2) Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |