Introduction to linear algebra:
Saved in:
| New Title: | Strang, Gilbert Introduction to linear algebra |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, MA
Wellesley-Cambridge Press
[2016]
|
| Edition: | Fifth edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | x, 574 Seiten Diagramme |
| ISBN: | 9780980232776 |
Staff View
MARC
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| 100 | 1 | |a Strang, Gilbert |d 1934- |0 (DE-588)141888474 |4 aut | |
| 245 | 1 | 0 | |a Introduction to linear algebra |c Gilbert Strang, Massachusetts Institute of Technology |
| 250 | |a Fifth edition | ||
| 264 | 1 | |a Wellesley, MA |b Wellesley-Cambridge Press |c [2016] | |
| 264 | 4 | |c © 2016 | |
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| 785 | 0 | 0 | |i Fortgesetzt durch |a Strang, Gilbert |t Introduction to linear algebra |b Fifth edition, revised printing, 2021 |z 978-1-7331466-5-4 |
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Record in the Search Index
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| adam_text | 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............................................. 46
2.3 Elimination Using Matrices.......................................... 58
2.4 Rules for Matrix Operations......................................... 70
2.5 Inverse Matrices.................................................... 83
2.6 Elimination = Factorization: A = LU................................. 97
2.7 Transposes and Permutations........................................ 109
3 Vector Spaces and Subspaces 123
3.1 Spaces of Vectors.................................................. 123
3.2 The Nullspace of A: Solving Ax = 0 and Rx = 0 ..................... 135
3.3 The Complete Solution to Ax = b............................. 150
3.4 Independence, Basis and Dimension.................................. 164
3.5 Dimensions of the Four Subspaces................................... 181
4 Orthogonality 194
4.1 Orthogonality of the Four Subspaces................................ 194
4.2 Projections ....................................................... 206
4.3 Least Squares Approximations....................................... 219
4.4 Orthonormal Bases and Gram-Schmidt................................. 233
5 Determinants 247
5.1 The Properties of Determinants..................................... 247
5.2 Permutations and Cofactors......................................... 258
5.3 Cramer’s Rule, Inverses, and Volumes............................... 273
■ * ■
III
IV Table of Contents
6 Eigenvaiues and Eigenvectors 288
6.1 Introduction to Eigenvalues....................................... 288
6.2 Diagonalizing a Matrix............................................ 304
6.3 Systems of Differential Equations................................ 319
6.4 Symmetric Matrices............................................... 338
6.5 Positive Definite Matrices........................................ 350
7 The Singular Value Decomposition (SVD) 364
7.1 Image Processing by Linear Algebra................................ 364
7.2 Bases and Matrices in the SVD..................................... 371
7.3 Principal Component Analysis (PCA by the SVD)..................... 382
7.4 The Geometry of the SVD........................................... 392
8 Linear Transformations 401
8.1 The Idea of a Linear Transformation............................... 401
8.2 The Matrix of a Linear Transformation............................. 411
8.3 The Search for a Good Basis....................................... 421
9 Complex Vectors and Matrices 430
9.1 Complex Numbers................................................... 431
9.2 Hermitian and Unitary Matrices.................................... 438
9.3 The Fast Fourier Transform........................................ 445
10 Applications 452
10.1 Graphs and Networks............................................... 452
10.2 Matrices in Engineering........................................... 462
10.3 Markov Matrices, Population, and Economics........................ 474
10.4 Linear Programming.............................................. 483
10.5 Fourier Series: Linear Algebra for Functions..................... 490
10.6 Computer Graphics................................................. 496
10.7 Linear Algebra for Cryptography.................................. 502
11 Numerical Linear Algebra 508
11.1 Gaussian Elimination in Practice.................................. 508
11.2 Norms and Condition Numbers....................................... 518
11.3 Iterative Methods and Preconditioners............................ 524
12 Linear Algebra in Probability Statistics 535
12.1 Mean, Variance, and Probability................................... 535
12.2 Covariance Matrices and Joint Probabilities...................... 546
12.3 Multivariate Gaussian and Weighted Least Squares.................. 555
Matrix Factorizations 563
Index 565
Six Great Theorems / Linear Algebra in a Nutshell 574
|
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| author | Strang, Gilbert 1934- |
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| author_facet | Strang, Gilbert 1934- |
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| bvnumber | BV043815755 |
| classification_rvk | SK 220 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)964067316 (DE-599)GBV868646539 |
| 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 | Fifth edition |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-20T06:43:21Z |
| institution | BVB |
| isbn | 9780980232776 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029226883 |
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| physical | x, 574 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Wellesley-Cambridge Press |
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| spellingShingle | Strang, Gilbert 1934- Introduction to linear algebra Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (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, Massachusetts Institute of Technology |
| title_fullStr | Introduction to linear algebra Gilbert Strang, Massachusetts Institute of Technology |
| title_full_unstemmed | Introduction to linear algebra Gilbert Strang, Massachusetts Institute of Technology |
| title_new | Strang, Gilbert Introduction to linear algebra |
| title_short | Introduction to linear algebra |
| title_sort | introduction to linear algebra |
| topic | Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029226883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| Call Number: |
2000 SK 220 S897(5) |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |
| Copy 2 | ausleihbar Available Place a Hold |