Introduction to linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wellesley, Mass.
Wellesley-Cambridge Press
2009
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 574 S. graph. Darst. |
| ISBN: | 9780980232714 9780980232721 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804138812841918464 |
|---|---|
| adam_text | Titel: Introduction to linear algebra
Autor: Strang, Gilbert
Jahr: 2009
Table of Contents
1 Introduction to Vectors 1
1.1 Vectors and Linear Combinations...................... 2
1.2 Lengths and Dot Products.......................... 11
1.3 Matrices................................... 22
2 Solving Linear Equations 31
2.1 Vectors and Linear Equations........................ 31
2.2 The Idea of Elimination........................... 45
2.3 Elimination Using Matrices......................... 56
2.4 Rules for Matrix Operations........................ 67
2.5 Inverse Matrices............................... 81
2.6 Elimination = Factorization: A = LU .................. 95
2.7 Transposes and Permutations........................ 107
3 Vector Spaces and Subspaces 120
3.1 Spaces of Vectors.............................. 120
3.2 The Nullspace of A: Solving Ax = 0................... 132
3.3 The Rank and the Row Reduced Form................... 144
3.4 The Complete Solution to Ax =b..................... 155
3.5 Independence, Basis and Dimension.................... 168
3.6 Dimensions of the Four Subspaces..................... 184
4 Orthogonality 195
4.1 Orthogonality of the Four Subspaces.................... 195
4.2 Projections ................................. 206
4.3 Least Squares Approximations....................... 218
4.4 Orthogonal Bases and Gram-Schmidt ................... 230
5 Determinants 244
5.1 The Properties of Determinants....................... 244
5.2 Permutations and Cofactors......................... 255
5.3 Cramer s Rule, Inverses, and Volumes................... 269
6 Eigenvalues and Eigenvectors 283
6.1 Introduction to Eigenvalues......................... 283
6.2 Diagonalizing a Matrix........................... 298
6.3 Applications to Differential Equations................... 312
6.4 Symmetric Matrices............................. 330
6.5 Positive Definite Matrices.......................... 342
6.6 Similar Matrices............................... 355
6.7 Singular Value Decomposition (SVD)................... 363
7 Linear Transformations 375
7.1 The Idea of a Linear Transformation.................... 375
7.2 The Matrix of a Linear Transformation................... 384
7.3 Diagonalization and the Pseudoinverse................... 399
8 Applications 409
8.1 Matrices in Engineering........................... 409
8.2 Graphs and Networks............................ 420
8.3 Markov Matrices, Population, and Economics............... 431
8.4 Linear Programming............................ 440
8.5 Fourier Series: Linear Algebra for Functions................ 447
8.6 Linear Algebra for Statistics and Probability................ 453
8.7 Computer Graphics............................. 459
9 Numerical Linear Algebra 465
9.1 Gaussian Elimination in Practice...................... 465
9.2 Norms and Condition Numbers....................... 475
9.3 Iterative Methods and Preconditioners................... 481
10 Complex Vectors and Matrices 493
10.1 Complex Numbers............................. 493
10.2 Hermitian and Unitary Matrices ...................... 501
10.3 The Fast Fourier Transform......................... 509
Solutions to Selected Exercises 516
Conceptual Questions for Review 552
Glossary: A Dictionary for Linear Algebra 557
Matrix Factorizations 564
Teaching Codes 566
Index 567
Linear Algebra in a Nutshell 574
|
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| dewey-full | 512.5 |
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| spelling | Strang, Gilbert 1934- Verfasser (DE-588)141888474 aut Introduction to linear algebra Gilbert Strang 4. ed. Wellesley, Mass. Wellesley-Cambridge Press 2009 IX, 574 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Álgebra linear larpcal Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017311178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Strang, Gilbert 1934- Introduction to linear algebra Álgebra linear larpcal Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Introduction to linear algebra |
| title_auth | Introduction to linear algebra |
| title_exact_search | Introduction to linear algebra |
| title_full | Introduction to linear algebra Gilbert Strang |
| title_fullStr | Introduction to linear algebra Gilbert Strang |
| title_full_unstemmed | Introduction to linear algebra Gilbert Strang |
| title_short | Introduction to linear algebra |
| title_sort | introduction to linear algebra |
| topic | Álgebra linear larpcal Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Álgebra linear Algebras, Linear Textbooks Lineare Algebra Einführung Lehrbuch |
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