Learning linear algebra through derive:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Prentice Hall
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 353 S. graph. Darst. |
| ISBN: | 0131226649 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Series Preface ix
Preface xi
Chapter 1 Matrices
1.1 The idea of a matrix 1
1.2 Addition of matrices 2
1.3 Some special matrices 7
1.4 Equality of matrices 8
1.5 Some more matrices 8
1.6 The algebra of matrices 10
1.7 Multiplication of matrices 12
1.8 Inverse of a matrix under addition and under multiplication 15
Chapter 2 Determinants
2.1 Linear equations in two unknowns 19
2.2 Linear equations in three or more unknowns 22
2.3 Cofactors and minors 28
2.4 Some results in determinant theory 32
Chapter 3 Vectors
3.1 Row and column vectors 40
3.2 Equality of vectors 43
3.3 Addition and multiplication of vectors 45
3.4 A geometrical alternative 47
3.5 Orthogonality of vectors 48
3.6 The vector product in 9l3 49
3.7 Applications to geometry 52
3.8 Linear dependence and independence of vectors 53
3.9 Further vector geometry 58
vi Contents
Chapter 4 More Matrices
4.1 Definitions 63
4.2 The multiplicative inverse revisited! 68
4.3 The adjoint or adjugate matrix 70
4.4 Stochastic matrices 76
4.5 Echelon matrices 76
4.6 Elementary row operations and row equivalence 77
4.7 Elementary matrices 79
4.8 The rank of a matrix 92
Chapter 5 Systems of Linear Equations
5.1 Recap from preceding chapters 101
5.2 Non-unique solutions 105
5.3 Homogeneous equations 111
5.4 Gaussian elimination 112
5.5 Pivotal condensation 119
5.6 Tabular method for Gaussian elimination 121
5.7 Ill-conditioning 123
5.8 Iterative method 128
Chapter 6 Vector Spaces and Linear Transformations
6.1 Vector spaces 138
6.2 Examples of vector spaces 143
6.3 Vector subspaces 146
6.4 Spans, frames and bases 147
6.5 The dimension of a vector space 150
6.6 The null space of a matrix 159
6.7 Linear transformations 166
6.8 Kernel and image of a linear transformation 174
6.9 Change of basis 184
6.10 Similarity 188
Chapter 7 Eigenvalues and Eigenvectors
7.1 Eigenvalues and eigenvectors 199
7.2 Eigenspaces 214
7.3 Some properties of eigenvalues 220
7.4 Diagonal ization revisited 228
Contents vii
Chapter 8 Orthogonal Matrices
8.1 Some reminders and definitions 236
8.2 Orthogonal bases 244
8.3 The Gram-Schmidt orthogonalization process 246
8.4 Symmetric matrices 252
8.5 QR decomposition 255
Chapter 9 Some Applications
9.1 Networks 261
9.2 Steady state and Markov processes 266
9.3 An application from economics 270
9.4 Coding and decoding messages 272
9.5 Quadratic forms and conic sections 273
9.6 Differential equations 280
Answers to Exercises and Solutions to Consolidation Exercises 290
Index of Definitions 345
Bibliography for Further Reading and Sources for More Exercises 346
Index 349
|
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| dewey-full | 512.5078 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5078 |
| dewey-search | 512.5078 |
| dewey-sort | 3512.5078 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV023762897 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:36:18Z |
| institution | BVB |
| isbn | 0131226649 |
| language | English |
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| physical | XII, 353 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Prentice Hall |
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| spelling | Denton, Brian Verfasser aut Learning linear algebra through derive Brain Denton London [u.a.] Prentice Hall 1995 XII, 353 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lineare Algebra (DE-588)4035811-2 gnd rswk-swf DERIVE (DE-588)4311492-1 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DERIVE (DE-588)4311492-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017405140&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Denton, Brian Learning linear algebra through derive Lineare Algebra (DE-588)4035811-2 gnd DERIVE (DE-588)4311492-1 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4311492-1 |
| title | Learning linear algebra through derive |
| title_auth | Learning linear algebra through derive |
| title_exact_search | Learning linear algebra through derive |
| title_full | Learning linear algebra through derive Brain Denton |
| title_fullStr | Learning linear algebra through derive Brain Denton |
| title_full_unstemmed | Learning linear algebra through derive Brain Denton |
| title_short | Learning linear algebra through derive |
| title_sort | learning linear algebra through derive |
| topic | Lineare Algebra (DE-588)4035811-2 gnd DERIVE (DE-588)4311492-1 gnd |
| topic_facet | Lineare Algebra DERIVE |
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