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Linear Dependence: Theory and Computation

S.N. Afriat
Format
Book
Published
New York : Kluwer Academic/Plenum Publishers, c2000.
Language
English
ISBN
0306464284
Contents
  • Chapter 1 Matrices
  • 1.1 Matrices and vectors 9
  • 1.2 Submatrices 10
  • 1.3 Matrix operations 12
  • 1.4 Algebra 15
  • 1.5 Vector space 17
  • Chapter 2 Linear Space
  • 2.2 Subspaces 23
  • 2.3 Span 25
  • 2.4 Direct sum 26
  • 2.5 Factor space 29
  • 2.6 Dual space 31
  • 2.7 Annihilators 32
  • 2.8 Direct product 33
  • 2.9 Algebra of subspaces 34
  • 2.10 Affine space 36
  • Chapter 3 Linear Dependence
  • 3.2 Replacement 41
  • 3.3 Rank 43
  • 3.4 Elementary operations 44
  • Chapter 4 Dimension
  • 4.1 Base 46
  • 4.3 Coordinates 49
  • 4.4 Dual base 51
  • 4.5 Annihilator dimension 52
  • 4.6 Affine coordinates 53
  • Chapter 5 Replacement
  • 5.1 Replacement algorithm 55
  • 5.2 Matrix rank 58
  • 5.3 Block replacement 60
  • 5.4 Extended table 63
  • 5.5 Condensed table 64
  • Chapter 6 Linear Equations
  • 6.1 Maximal replacement 67
  • 6.2 Gaussian elimination 71
  • 6.3 Rank reduction 73
  • 6.4 Echelon form 77
  • 6.5 Pivotal condensation 78
  • 6.6 Tucker scheme 81
  • Chapter 7 Determinants
  • 7.1 Solution characteristics 89
  • 7.2 Determinants 90
  • 7.3 Adjoint and inverse 94
  • 7.4 Derived system 95
  • 7.5 Double determinants 97
  • 7.6 Alternants 99
  • Chapter 8 Determinants and Matrices
  • 8.1 Partitioned determinants 104
  • 8.2 Partitioned inverse 107
  • 8.3 Principal minors 110
  • Chapter 9 Quadratic Forms
  • 9.1 Symmetric matrices 111
  • 9.3 Definite forms 113
  • 9.4 Completing the square 114
  • 9.5 Semidefinite forms 116
  • 9.6 Linear restrictions 117
  • 9.7 Finsler's theorem 120
  • 1 Permutations 127
  • 2 Combinations 131
  • BASIC Programs
  • 1 Maximal replacement 138
  • 2 Rank reduction 143
  • 3 Tucker's pivot algorithm 144
  • 4 Extended rank reduction 150
  • 5 Permutations 157
  • 6 Combinations 160.
Description
xv, 175 p. : ill. ; 24 cm.
Notes
Includes bibliographical references (p. 165-169) and index.
Technical Details
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    a| Linear dependence : b| theory and computation / c| S.N. Afriat.
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    g| Chapter 1 t| Matrices -- g| 1.1 t| Matrices and vectors g| 9 -- g| 1.2 t| Submatrices g| 10 -- g| 1.3 t| Matrix operations g| 12 -- g| 1.4 t| Algebra g| 15 -- g| 1.5 t| Vector space g| 17 -- g| Chapter 2 t| Linear Space -- g| 2.2 t| Subspaces g| 23 -- g| 2.3 t| Span g| 25 -- g| 2.4 t| Direct sum g| 26 -- g| 2.5 t| Factor space g| 29 -- g| 2.6 t| Dual space g| 31 -- g| 2.7 t| Annihilators g| 32 -- g| 2.8 t| Direct product g| 33 -- g| 2.9 t| Algebra of subspaces g| 34 -- g| 2.10 t| Affine space g| 36 -- g| Chapter 3 t| Linear Dependence -- g| 3.2 t| Replacement g| 41 -- g| 3.3 t| Rank g| 43 -- g| 3.4 t| Elementary operations g| 44 -- g| Chapter 4 t| Dimension -- g| 4.1 t| Base g| 46 -- g| 4.3 t| Coordinates g| 49 -- g| 4.4 t| Dual base g| 51 -- g| 4.5 t| Annihilator dimension g| 52 -- g| 4.6 t| Affine coordinates g| 53 -- g| Chapter 5 t| Replacement -- g| 5.1 t| Replacement algorithm g| 55 -- g| 5.2 t| Matrix rank g| 58 -- g| 5.3 t| Block replacement g| 60 -- g| 5.4 t| Extended table g| 63 -- g| 5.5 t| Condensed table g| 64 -- g| Chapter 6 t| Linear Equations -- g| 6.1 t| Maximal replacement g| 67 -- g| 6.2 t| Gaussian elimination g| 71 -- g| 6.3 t| Rank reduction g| 73 -- g| 6.4 t| Echelon form g| 77 -- g| 6.5 t| Pivotal condensation g| 78 -- g| 6.6 t| Tucker scheme g| 81 -- g| Chapter 7 t| Determinants -- g| 7.1 t| Solution characteristics g| 89 -- g| 7.2 t| Determinants g| 90 -- g| 7.3 t| Adjoint and inverse g| 94 -- g| 7.4 t| Derived system g| 95 -- g| 7.5 t| Double determinants g| 97 -- g| 7.6 t| Alternants g| 99 -- g| Chapter 8 t| Determinants and Matrices -- g| 8.1 t| Partitioned determinants g| 104 -- g| 8.2 t| Partitioned inverse g| 107 -- g| 8.3 t| Principal minors g| 110 -- g| Chapter 9 t| Quadratic Forms -- g| 9.1 t| Symmetric matrices g| 111 -- g| 9.3 t| Definite forms g| 113 -- g| 9.4 t| Completing the square g| 114 -- g| 9.5 t| Semidefinite forms g| 116 -- g| 9.6 t| Linear restrictions g| 117 -- g| 9.7 t| Finsler's theorem g| 120 -- g| 1 t| Permutations g| 127 -- g| 2 t| Combinations g| 131 -- t| BASIC Programs -- g| 1 t| Maximal replacement g| 138 -- g| 2 t| Rank reduction g| 143 -- g| 3 t| Tucker's pivot algorithm g| 144 -- g| 4 t| Extended rank reduction g| 150 -- g| 5 t| Permutations g| 157 -- g| 6 t| Combinations g| 160.
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