Introduction to linear algebra:
Gespeichert in:
| Vorheriger Titel: | Strang, Gilbert Introduction to linear algebra |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wellesley
Wellesley-Cambridge Press
[2021]
|
| Ausgabe: | Fifth edition, revised printing |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Website for this Book: math.mit.edu/linearalgebra Zoom notes (new in 2021): math.mit.edu/ZoomNotes Weiteres Material: web.mit.edu/18.06 Originally published: Wellesley: Wellesley-Cambridge Press, 2016 ; Auf der Rückseite des Titels: "The revised printing has online Zoomnotes and open format / no shading and a new ISBN" |
| Beschreibung: | x, 573 Seiten Illustrationen |
| ISBN: | 9781733146654 1733146652 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to linear algebra |c Gilbert Strang, Massachusetts Institute of Technology |
| 250 | |a Fifth edition, revised printing | ||
| 264 | 1 | |a Wellesley |b Wellesley-Cambridge Press |c [2021] | |
| 300 | |a x, 573 Seiten |b Illustrationen | ||
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| 500 | |a Zoom notes (new in 2021): math.mit.edu/ZoomNotes | ||
| 500 | |a Weiteres Material: web.mit.edu/18.06 | ||
| 500 | |a Originally published: Wellesley: Wellesley-Cambridge Press, 2016 ; Auf der Rückseite des Titels: "The revised printing has online Zoomnotes and open format / no shading and a new ISBN" | ||
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents 1 Introduction to Vectors 1.1 Vectors and Linear Combinations................................................................ 1.2 Lengths and Dot Products........................................................................... 1.3 Matrices..................................................................................................... 1 2 11 22 2 Solving Linear Equations 2.1 Vectors and Linear Equations.................................................................... 2.2 The Idea of Elimination............................................................................. 2.3 Elimination Using Matrices....................................................................... 2.4 Rules for Matrix Operations .................................................................... 2.5 Inverse Matrices......................................................................................... 2.6 Elimination = Factorization: A =LU.................................................... 2.7 Transposes and Permutations.................................................................... 31 31 46 58 70 83 97 108 3 Vector Spaces and Subspaces 3.1 Spaces of Vectors...................................................................................... 3.2 The Nullspace of A: Solving Ax =0 and Rx = 0 ............................... 3.3 The Complete Solution to Ax = b........................................................... 3.4 Independence, Basis and Dimension......................................................... 3.5 Dimensions of the Four
Subspaces........................................................... 122 122 134 149 163 180 4 Orthogonality 4.1 Orthogonality of the Four Subspaces........................................................ 4.2 Projections ............................................................................................... 4.3 Least Squares Approximations................................................................. 4.4 Orthonormal Bases and Gram-Schmidt..................................................... 193 193 205 218 232 5 246 246 257 272 Determinants 5.1 The Properties of Determinants................................................................. 5.2 Permutations and Cofactors........................................................................ 5.3 Cramer’s Rule, Inverses, and Volumes...................................................... ІІІ
İV 6 Table of Contents Eigenvalues and Eigenvectors 6.1 Introduction to Eigenvalues........................................................................ 6.2 Diagonalizing a Matrix............................................................................... 6.3 Systems of Differential Equations ............................................................ 6.4 Symmetric Matrices..................................................................................... 6.5 Positive Definite Matrices........................................................................... 7 The 7.1 7.2 7.3 7.4 287 287 303 318 337 349 Singular Value Decomposition (SVD) Image Processing by Linear Algebra......................................................... Bases and Matrices in the SVD.................................................................. Principal Component Analysis (PCA by the SVD).................................... The Geometry of the SVD........................................................................ 363 363 370 381 391 8 Linear Transformations 8.1 The Idea of a Linear Transformation......................................................... 8.2 The Matrix of a Linear Transformation...................................................... 8.3 The Search for a Good Basis..................................................................... 400 400 410 420 9 Complex Vectors and Matrices 9.1 Complex Numbers ..................................................................................... 9.2 Hermitian and Unitary Matrices
............................................................... 9.3 The Last Lourier Transform........................................................................ 429 430 437 444 10 Applications 10.1 Graphs and Networks................................................................................. 10.2 Matrices in Engineering.............................................................................. 10.3 Markov Matrices, Population, and Economics.......................................... 10.4 Linear Programming................................................................................. 10.5 Lourier Series: Linear Algebra for Lunctions............................................. 10.6 Computer Graphics.................................................................................... 10.7 Linear Algebra for Cryptography...................................... 451 451 461 473 482 489 495 501 11 Numerical Linear Algebra 11.1 Gaussian Elimination in Practice............................................................... 11.2 Norms and Condition Numbers.................................................................. 11.3 Iterative Methods and Preconditioners...................................................... 507 507 517 523 12 Linear Algebra in Probability Statistics 12.1 Mean, Variance, and Probability............................................................... 12.2 Covariance Matrices and Joint Probabilities............................................. 12.3 Multivariate Gaussian and Weighted Least Squares................................. 534 534 545 554
Matrix Factorizations 562 Index 564 Six Great Theorems / LinearAlgebra in a Nutshell 573
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| adam_txt |
Table of Contents 1 Introduction to Vectors 1.1 Vectors and Linear Combinations. 1.2 Lengths and Dot Products. 1.3 Matrices. 1 2 11 22 2 Solving Linear Equations 2.1 Vectors and Linear Equations. 2.2 The Idea of Elimination. 2.3 Elimination Using Matrices. 2.4 Rules for Matrix Operations . 2.5 Inverse Matrices. 2.6 Elimination = Factorization: A =LU. 2.7 Transposes and Permutations. 31 31 46 58 70 83 97 108 3 Vector Spaces and Subspaces 3.1 Spaces of Vectors. 3.2 The Nullspace of A: Solving Ax =0 and Rx = 0 . 3.3 The Complete Solution to Ax = b. 3.4 Independence, Basis and Dimension. 3.5 Dimensions of the Four
Subspaces. 122 122 134 149 163 180 4 Orthogonality 4.1 Orthogonality of the Four Subspaces. 4.2 Projections . 4.3 Least Squares Approximations. 4.4 Orthonormal Bases and Gram-Schmidt. 193 193 205 218 232 5 246 246 257 272 Determinants 5.1 The Properties of Determinants. 5.2 Permutations and Cofactors. 5.3 Cramer’s Rule, Inverses, and Volumes. ІІІ
İV 6 Table of Contents Eigenvalues and Eigenvectors 6.1 Introduction to Eigenvalues. 6.2 Diagonalizing a Matrix. 6.3 Systems of Differential Equations . 6.4 Symmetric Matrices. 6.5 Positive Definite Matrices. 7 The 7.1 7.2 7.3 7.4 287 287 303 318 337 349 Singular Value Decomposition (SVD) Image Processing by Linear Algebra. Bases and Matrices in the SVD. Principal Component Analysis (PCA by the SVD). The Geometry of the SVD. 363 363 370 381 391 8 Linear Transformations 8.1 The Idea of a Linear Transformation. 8.2 The Matrix of a Linear Transformation. 8.3 The Search for a Good Basis. 400 400 410 420 9 Complex Vectors and Matrices 9.1 Complex Numbers . 9.2 Hermitian and Unitary Matrices
. 9.3 The Last Lourier Transform. 429 430 437 444 10 Applications 10.1 Graphs and Networks. 10.2 Matrices in Engineering. 10.3 Markov Matrices, Population, and Economics. 10.4 Linear Programming. 10.5 Lourier Series: Linear Algebra for Lunctions. 10.6 Computer Graphics. 10.7 Linear Algebra for Cryptography. 451 451 461 473 482 489 495 501 11 Numerical Linear Algebra 11.1 Gaussian Elimination in Practice. 11.2 Norms and Condition Numbers. 11.3 Iterative Methods and Preconditioners. 507 507 517 523 12 Linear Algebra in Probability Statistics 12.1 Mean, Variance, and Probability. 12.2 Covariance Matrices and Joint Probabilities. 12.3 Multivariate Gaussian and Weighted Least Squares. 534 534 545 554
Matrix Factorizations 562 Index 564 Six Great Theorems / LinearAlgebra in a Nutshell 573 |
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| illustrated | Illustrated |
| index_date | 2024-07-03T18:13:09Z |
| indexdate | 2024-07-10T09:13:20Z |
| institution | BVB |
| isbn | 9781733146654 1733146652 |
| language | English |
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| spelling | Strang, Gilbert 1934- Verfasser (DE-588)141888474 aut Introduction to linear algebra Gilbert Strang, Massachusetts Institute of Technology Fifth edition, revised printing Wellesley Wellesley-Cambridge Press [2021] x, 573 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Website for this Book: math.mit.edu/linearalgebra Zoom notes (new in 2021): math.mit.edu/ZoomNotes Weiteres Material: web.mit.edu/18.06 Originally published: Wellesley: Wellesley-Cambridge Press, 2016 ; Auf der Rückseite des Titels: "The revised printing has online Zoomnotes and open format / no shading and a new ISBN" Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Algebras, Linear Algebras, Linear / Problems, exercises, etc Problems and exercises Lineare Algebra (DE-588)4035811-2 s DE-604 Vorangegangen ist Strang, Gilbert Introduction to linear algebra 5th edition 978-0-9802327-7-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032884176&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strang, Gilbert 1934- Introduction to linear algebra Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Introduction to linear algebra |
| title_auth | Introduction to linear algebra |
| title_exact_search | Introduction to linear algebra |
| title_exact_search_txtP | 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_old | 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 |
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