Applied linear algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice-Hall
1977
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 477 S. graph. Darst. |
| ISBN: | 0130413437 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applied linear algebra |c Ben Noble ; James W. Daniel |
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Record in the Search Index
| _version_ | 1804116370175033344 |
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| adam_text | Titel: Applied linear algebra
Autor: Noble, Ben
Jahr: 1977
CONTENTS Preface Common Notation 1 Matrix Algebra 1.1 Introduction, 1 1.2 Equality, addition, and multiplication by a scalar, 3 1.3 The multiplication of matrices, 6 1.4 The inverse matrix, 14 1.5 The partitioning of matrices, 21 Miscellaneous exercises 1, 24 2 Some Simple Applications of Matrices 2.1 Introduction, 30 2.2 A Markov-chain example, 31 2.3 A simple model of growth, 39
viii ? Contents 2.4 A plane pin-jointed framework, 43 2.5 Production planning, 51 2.6 The method of least squares, 57 Miscellaneous exercises 2, 63 3 Simultaneous Linear Equations and Elementary Operations 66 3.1 Introduction, 66 3.2 The method of Gauss (or successive) elimination, 67 3.3 The existence of solutions for a set of equations: Some examples, 76 3.4 Row operations to simplify matrices and sets of equations, 80 3.5 Row-echelon form and rank, 88 3.6 Solution sets for equations; the Fredholm Alternative, 91 3.7 Inverses of matrices, 95 Miscellaneous exercises 3, 97 4 Vectors and Vector Spaces 102 4.1 Geometrical vectors in three-dimensional space, 102 4.2 General vector spaces, 107 4.3 Linear dependence and independence, 112 4.4 Basis and dimension, 118 4.5 Matrices, rank, basis, and dimension, 123 4.6 Vector norms, 130 4.7 Inner products and orthogonality, 133 Miscellaneous exercises 4, 143 5 Matrices and Linear Transformations 150 5.1 Linear transformations, 150 5.2 Equations and inverses, 154 5.3 Norms of matrices and linear transformations, 163 5.4 Inverses of perturbed matrices, 168 5.5 Condition of linear equations, 170 Miscellaneous exercises 5, 174 6 Practical Solution of Systems of Equations 177 6.1 Introduction, 177 6.2 Gauss elimination, 179 6.3 The choice of pivots in elimination, 184
Contents ? ix 6.4 Solving slightly modified systems, 191 6.5 Determinants, 198 6.6 Determinantal representation of solutions and inverses, 205 Miscellaneous exercises 6, 209 7 Linear Programming 213 7.1 The simplex method: An example, 213 7.2 The general linear program, 220 7.3 The simplex method in general, 225 7.4 Complications for the simplex method, 232 7.5 Duality, 244 Miscellaneous exercises 7, 253 8 Eigenvalues and Eigenvectors: An Overview 256 8.1 Introduction, 256 8.2 Definitions and basic properties, 263 8.3 Eigensystems, decompositions, and transformations, 271 8.4 Similarity transformations, 278 8.5 Unitary matrices and transformations, 282 8.6 The condition of eigensystems, 289 Miscellaneous exercises 8, 295 9 Unitary Transformations, Eigensystems, and Applications 301 9.1 Introduction, 301 9.2 Schur decomposition or canonical form, 302 9.3 Eigensystems of normal matrices, 307 9.4 The QR decomposition, 315 9.5 The singular-value decomposition, 323 9.6 Least squares and the generalized inverse, 330 9.7 Analyzing influential factors in experiments, 342 Miscellaneous exercises 9, 346 10 Similarity Transformations, Eigensystems, and Applications 10.1 Introduction, 351 10.2 Defective matrices: Examples and their meanings, 10.3 Jordan form of an n x n matrix, 358 10.4 Jordan form and eigensystems of general matrices, 351 353 367
X ? Contents 10.5 Discrete system evolution and powers of matrices, 374 10.6 Iterative solution of linear equations, 383 10.7 Continuous system evolution and matrix exponentials, 393 Miscellaneous exercises 10, 403 11 Quadratic Forms and Variational Principles 11.1 Introduction, 408 11.2 A geometric example, 410 11.3 General quadratic forms, 418 11.4 Definite quadratic forms, 425 11.5 Extremizing quadratic forms: Rayleigh’s Principle, 429 11.6 Extremizing quadratic forms: The Min-max Principle, 436 Miscellaneous exercises 11, 442 Appendix 1 Hints and Answers to Selected Exercises Appendix 2 Bibliography Index to Numbered Statements 408 447 459 465 Index
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:26Z |
| institution | BVB |
| isbn | 0130413437 |
| language | English |
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| physical | XVII, 477 S. graph. Darst. |
| publishDate | 1977 |
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| spelling | Noble, Ben Verfasser aut Applied linear algebra Ben Noble ; James W. Daniel 2. ed. Englewood Cliffs, NJ Prentice-Hall 1977 XVII, 477 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Álgebra linear larpcal Álgebra larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Daniel, James W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258363&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noble, Ben Daniel, James W. Applied linear algebra Algèbre linéaire Álgebra linear larpcal Álgebra larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Applied linear algebra |
| title_auth | Applied linear algebra |
| title_exact_search | Applied linear algebra |
| title_full | Applied linear algebra Ben Noble ; James W. Daniel |
| title_fullStr | Applied linear algebra Ben Noble ; James W. Daniel |
| title_full_unstemmed | Applied linear algebra Ben Noble ; James W. Daniel |
| title_short | Applied linear algebra |
| title_sort | applied linear algebra |
| topic | Algèbre linéaire Álgebra linear larpcal Álgebra larpcal Algebras, Linear Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algèbre linéaire Álgebra linear Álgebra Algebras, Linear Lineare Algebra |
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