Applied linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1987
|
| Series: | Pure and applied mathematics
105 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 258 S. |
| ISBN: | 0824776224 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ijj
1. Vector Spaces 1
1.1 Fields 1
1.2 Vector Spaces 4
1.3 Matrices 9
1.4 Other Examples of Vector Spaces ] l
1.5 Subspaces 13
1.6 Linear Dependence, Basis, and Dimension 16
1.7 Linear Dependence of a Set of Functions 20
1.8 Vector Norms and Inner Products 22
2. Matrices 26
2.1 Product of Two Matrices 26
2.2 The Operation of Transposition 34
2.3 Inversion 37
2.4 Inverses for Some Special Matrices: Band Matrices 45
2.5 The Row and Column Spaces of a Matrix,
Nullspace of a Matrix, Elementary Matrices 54
3. Generalized Inverses 65
3.1 Right and Left Inverses 65
3.2 Principle of Least Squares 72
3.3 Matrix Methods for Least Squares Problems 81
3.4 The Moore Penrose Inverse 84
v
vi Contents
4. Linear Transformations 101
4.1 Definition and Examples 101
4.2 The Matrix of a Linear Transformation 108
4.3 Transition Matrix and Change of Basis 115
5. The Eigenvalue Problem 123
5.1 Eigenvalues and Eigenvectors 123
5.2 Eigenvalues of Some Special Matrices 135
5.3 Spectral Theorem 143
5.4 Jordan s Canonical Form 148
5.5 Positive Definite Matrices 160
6. Functions of a Matrix 170
6.1 Introduction 170
6.2 Functions of a Matrix Defined by a Power Series 179
6.3 Evaluation of exp(zA) by the Laplace Transform Method 187
7. Irreducible and Monotone Matrices 194
7.1 Irreducible Matrices 194
7.2 Monotone Matrices 202
7.3 Application to the Two Point Linear Boundary Value Problem 205
7.4 Nonlinear Two Point Boundary Value Problem 209
Appendix: Determinants and Linear Equations 212
1. Determinants 212
2. Linear Equations 216
Miscellaneous Exercises 222
Bibliography 231
Answers 233
Index 255
|
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| id | DE-604.BV000640133 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:02Z |
| institution | BVB |
| isbn | 0824776224 |
| language | English |
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| physical | VI, 258 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Usmani, Riaz A. Verfasser aut Applied linear algebra Riaz A. Usmani New York [u.a.] Dekker 1987 VI, 258 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 105 Lineare Algebra Anwendung (DE-588)4196864-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Anwendung (DE-588)4196864-5 s DE-604 Pure and applied mathematics 105 (DE-604)BV000001885 105 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000398729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Usmani, Riaz A. Applied linear algebra Pure and applied mathematics Lineare Algebra Anwendung (DE-588)4196864-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4035811-2 |
| title | Applied linear algebra |
| title_auth | Applied linear algebra |
| title_exact_search | Applied linear algebra |
| title_full | Applied linear algebra Riaz A. Usmani |
| title_fullStr | Applied linear algebra Riaz A. Usmani |
| title_full_unstemmed | Applied linear algebra Riaz A. Usmani |
| title_short | Applied linear algebra |
| title_sort | applied linear algebra |
| topic | Lineare Algebra Anwendung (DE-588)4196864-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra Anwendung |
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