Principles of linear algebra with Maple:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, New Jersey
Wiley
2010
|
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 596 S. graph. Darst. |
| ISBN: | 9780470637593 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Principles of linear algebra with Maple
Autor: Shiskowski, Kenneth
Jahr: 2010
Contents
Preface ix
Conventions and Notations xiv
TM
1 An Introduction To Maple 1
1.1 The Commands........................... 2
1.2 Programming............................ 11
2 Linear Systems of Equations and Matrices 15
2.1 Linear Systems of Equations.................... 15
2.2 Augmented Matrix of a Linear System and Row Operations . . 28
2.3 Some Matrix Arithmetic...................... 39
3 Gauss-Jordan Elimination and Reduced Row Echelon Form 51
3.1 Gauss-Jordan Elimination and rref................ 51
3.2 Elementary Matrices........................ 65
3.3 Sensitivity of Solutions to Error in the Linear System..... 74
4 Applications of Linear Systems and Matrices 89
4.1 Applications of Linear Systems to Geometry........... 89
4.2 Applications of Linear Systems to Curve Fitting ........ 99
4.3 Applications of Linear Systems to Economics.......... 107
4.4 Applications of Matrix Multiplication to Geometry....... 112
4.5 An Application of Matrix Multiplication to Economics..... 120
5 Determinants, Inverses, and Cramer s Rule 129
5.1 Determinants and Inverses from the Adjoint Formula...... 129
5.2 Determinants by Expanding Along Any Row or Column .... 147
5.3 Determinants Found by Triangularizing Matrices........ 159
5.4 LU Factorization.......................... 171
5.5 Inverses from rref ......................... 179
5.6 Cramer s Rule............................ 184
vi Contents
6 Basic Linear Algebra Topics 195
6.1 Vectors ............................... 195
6.2 Dot Product............................. 210
6.3 Cross Product............................ 223
6.4 Vector Projection.......................... 232
7 A Few Advanced Linear Algebra Topics 245
7.1 Rotations in Space......................... 245
7.2 Rolling a Circle Along a Curve................. 255
7.3 The TNB Frame.......................... 265
8 Independence, Basis, and Dimension for Subspaces
of Rn 271
8.1 Subspaces of R™ .......................... 271
8.2 Independent and Dependent Sets of Vectors in Rn ....... 289
8.3 Basis and Dimension for Subspaces of R ............ 302
8.4 Vector Projection onto a Subspace of K ............. 311
8.5 The Gram-Schmidt Orthonormalization Process......... 322
9 Linear Maps from Rn to Rm 333
9.1 Basics About Linear Maps..................... 333
9.2 The Kernel and Image Subspaces of a Linear Map....... 345
9.3 Composites of Two Linear Maps and Inverses.......... 354
9.4 Change of Bases for the Matrix Representation
of a Linear Map........................... 361
10 The Geometry of Linear and Affine Maps 375
10.1 The Effect of a Linear Map on Area and Arclength
in Two Dimensions......................... 375
10.2 The Decomposition of Linear Maps into Rotations,
Reflections, and Rescalings in R2................. 393
10.3 The Effect of Linear Maps on Volume, Area,
and Arclength in R3........................ 401
10.4 Rotations, Reflections, and Rescalings in Three Dimensions . . 412
10.5 Affine Maps............................. 423
11 Least-Squares Fits and Pseudoinverses 435
11.1 Pseudoinverse to a Nonsquare Matrix and Almost Solving
an Overdetermined Linear System................ 435
11.2 Fits and Pseudoinverses...................... 446
11.3 Least-Squares Fits and Pseudoinverses.............. 462
Contents vii
12 Eigenvalues and Eigenvectors 473
12.1 What Are Eigenvalues and Eigenvectors, and Why Do
We Need Them?.......................... 473
12.2 Summary of Definitions and Methods for Computing
Eigenvalues and Eigenvectors as well as the Exponential
of a Matrix............................. 488
12.3 Applications of the Diagonalizability of Square Matrices .... 492
12.4 Solving a Square First-Order Linear System of Differential
Equations.............................. 509
12.5 Basic Facts About Eigenvalues, Eigenvectors, and
Diagonalizability.......................... 551
12.6 The Geometry of the Ellipse Using Eigenvalues and
Eigenvectors............................. 565
12.7 A Maple Eigen-Procedure..................... 585
Suggested Reading 589
Indices 591
Keyword Index.............................. 591
Index of Maple Commands and Packages ............... 595
|
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| id | DE-604.BV040536121 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:26:00Z |
| institution | BVB |
| isbn | 9780470637593 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025382117 |
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| owner | DE-92 |
| owner_facet | DE-92 |
| physical | XIV, 596 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Shiskowski, Kenneth 1954- Verfasser (DE-588)142902241 aut Principles of linear algebra with Maple Kenneth Shiskowski ; Karl Frinkle Hoboken, New Jersey Wiley 2010 XIV, 596 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Maple Programm (DE-588)4209397-1 s DE-604 Frinkle, Karl 1977- Verfasser (DE-588)142902314 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025382117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shiskowski, Kenneth 1954- Frinkle, Karl 1977- Principles of linear algebra with Maple Lineare Algebra (DE-588)4035811-2 gnd Maple Programm (DE-588)4209397-1 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4209397-1 |
| title | Principles of linear algebra with Maple |
| title_auth | Principles of linear algebra with Maple |
| title_exact_search | Principles of linear algebra with Maple |
| title_full | Principles of linear algebra with Maple Kenneth Shiskowski ; Karl Frinkle |
| title_fullStr | Principles of linear algebra with Maple Kenneth Shiskowski ; Karl Frinkle |
| title_full_unstemmed | Principles of linear algebra with Maple Kenneth Shiskowski ; Karl Frinkle |
| title_short | Principles of linear algebra with Maple |
| title_sort | principles of linear algebra with maple |
| topic | Lineare Algebra (DE-588)4035811-2 gnd Maple Programm (DE-588)4209397-1 gnd |
| topic_facet | Lineare Algebra Maple Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025382117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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