Applied linear algebra / Ben Noble and James W. Daniel.
Editor: Englewood Cliffs, NJ : Prentice-Hall, c1988Edición: 3rd edDescripción: xvi, 521 p. : il. ; 25 cmISBN: 0130412600Tema(s): Algebras, LinearOtra clasificación: 15-01Chapter 1: MATRIX ALGEBRA [1] 1.1 Introduction [1] 1.2 Equality, addition, and multiplication by a scalar [3] 1.3 Matrix multiplication [8] 1.4 Matrix inverses [21] 1.5 Partitioned matrices [33] 1.6 Miscellaneous problems [40] Chapter 2: SOME SIMPLE APPLICATIONS AND QUESTIONS [42] 2.1 Introduction [42] 2.2 Business competition: Markov chains [43] 2.3 Population growth: powers of a matrix [50] 2.4 Equilibrium in networks: linear equations [54] 2.5 Oscillatory systems: eigenvalues [60] 2.6 General modeling: least squares [66] 2.7 Production planning: linear programs [73] 2.8 Miscellaneous problems [79] Chapter 3: SOLVING EQUATIONS AND FINDING INVERSES: METHODS [82] 3.1 Introduction [82] 3.2 Solving equations by Gauss elimination [83] 3.3 Existence of solutions to systems of equations: some examples and procedures [95] 3.4 Finding inverses by Gauss elimination [100] 3.5 Row operations and elementary matrices [103] 3.6 Choosing pivots for Gauss elimination in practice [107] 3.7 The LU-decomposition [116] 3.8 Work measures and solving slightly modified systems [125] 3.9 Computer software for Gauss elimination [134] 3.10 Miscellaneous problems [136] Chapter 4: SOLVING EQUATIONS AND FINDING INVERSES: THEORY [139] 4.1 Introduction [139] 4.2 Gauss-reduced form and rank [140] 4.3 Solvability and solution sets for systems of equations [147] 4.4 Inverses and rank [755] 4.5 Determinants and their properties [158] 4.6 Determinantal representation of inverses and solutions [167] 4.7 Miscellaneous problems [172] Chapter 5: VECTORS AND VECTOR SPACES [175] 5.1 Introduction; geometrical vectors [175] 5.2 General vector spaces [181] 5.3 Linear dependence and linear independence [187] 5.4 Basis, dimension, and coordinates [195] 5.5 Bases and matrices [207] 5.6 Length and distance in vector spaces: norms [275] 5.7 Angle in vector spaces: inner products [220] 5.8 Orthogonal projections and bases: general spaces and Gram-Schmidt [226] 5.9 Orthogonal projections and bases: Rp, Cp, QR, and least squares [234] 5.10 Miscellaneous problems [246] Chapter 6: LINEAR TRANSFORMATIONS AND MATRICES [249] 6.1 Introduction; linear transformations [249] 6.2 Matrix representations of linear transformations [257] 6.3 Norms of linear transformations and matrices [263] 6.4 Inverses of perturbed matrices; condition of linear equations [268] 6.5 Miscellaneous problems [277] Chapter 7: EIGENVALUES AND EIGENVECTORS: AN OVERVIEW [279] 7.1 Introduction [279] 7.2 Definitions and basic properties [284] 7.3 Eigensystems, decompositions, and transformation representations [293] 7.4 Similarity transformations; Jordan form [299] 7.5 Unitary matrices and unitary similarity; Schur and diagonal forms [304] 7.6 Computer software for finding eigensystems [315] 7.7 Condition of eigensystems [317] 7.8 Miscellaneous problems [322] Chapter 8: EIGENSYSTEMS OF SYMMETRIC, HERMITIAN, AND NORMAL MATRICES, WITH APPLICATIONS [325] 8.1 Introduction [325] 8.2 Schur form and decomposition; normal matrices [326] 8.3 Eigensystems of normal matrices [331] 8.4 Application: singular value decomposition [338] 8.5 Application: least squares and the pseudoinverse [346] 8.6 Miscellaneous problems [353] Chapter 9: EIGENSYSTEMS OF GENERAL MATRICES, WITH APPLICATIONS [355] 9.1 Introduction [355] 9.2 Jordan form [357] 9.3 Eigensystems for general matrices [364] 9.4 Application: discrete system evolution and matrix powers [369] 9.5 Application: continuous system evolution and matrix exponentials [378] 9.6 Application: iterative solution of linear equations [388] 9.7 Miscellaneous problems [395] Chapter 10: QUADRATIC FORMS AND VARIATIONAL CHARACTERIZATIONS OF EIGENVALUES [398] 10.1 Introduction [398] 10.2 Quadratic forms in R2 [400] 10.3 Quadratic forms in Rp and Cp [407] 10.4 Extremizing quadratic forms: Rayleigh’s principle [415] 10.5 Extremizing quadratic forms: the min-max principle [423] 10.6 Miscellaneous problems [428] Chapter 11: LINEAR PROGRAMMING [433] 11.1 Analysis of a simple example [433] 11.2 A general linear program [448] 11.3 Solving a general linear program [454] 11.4 Duality [465] 11.5 Miscellaneous problems [475] Appendix 1: ANSWERS AND AIDS TO SELECTED PROBLEMS [479] Appendix 2: BIBLIOGRAPHY [502] INDEX OF NOTATION [505] SUBJECT INDEX [509]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 15 N747 (Browse shelf) | Available | A-6862 |
Incluye índices.
Bibliografía: p. 502-504.
Chapter 1: --
MATRIX ALGEBRA [1] --
1.1 Introduction [1] --
1.2 Equality, addition, and multiplication by a scalar [3] --
1.3 Matrix multiplication [8] --
1.4 Matrix inverses [21] --
1.5 Partitioned matrices [33] --
1.6 Miscellaneous problems [40] --
Chapter 2: --
SOME SIMPLE APPLICATIONS AND QUESTIONS [42] --
2.1 Introduction [42] --
2.2 Business competition: Markov chains [43] --
2.3 Population growth: powers of a matrix [50] --
2.4 Equilibrium in networks: linear equations [54] --
2.5 Oscillatory systems: eigenvalues [60] --
2.6 General modeling: least squares [66] --
2.7 Production planning: linear programs [73] --
2.8 Miscellaneous problems [79] --
Chapter 3: SOLVING EQUATIONS AND FINDING INVERSES: METHODS [82] --
3.1 Introduction [82] --
3.2 Solving equations by Gauss elimination [83] --
3.3 Existence of solutions to systems of equations: some examples and procedures [95] --
3.4 Finding inverses by Gauss elimination [100] --
3.5 Row operations and elementary matrices [103] --
3.6 Choosing pivots for Gauss elimination in practice [107] --
3.7 The LU-decomposition [116] --
3.8 Work measures and solving slightly modified systems [125] --
3.9 Computer software for Gauss elimination [134] --
3.10 Miscellaneous problems [136] --
Chapter 4: SOLVING EQUATIONS AND FINDING INVERSES: THEORY [139] --
4.1 Introduction [139] --
4.2 Gauss-reduced form and rank [140] --
4.3 Solvability and solution sets for systems of equations [147] --
4.4 Inverses and rank [755] --
4.5 Determinants and their properties [158] --
4.6 Determinantal representation of inverses and solutions [167] --
4.7 Miscellaneous problems [172] --
Chapter 5: VECTORS AND VECTOR SPACES [175] --
5.1 Introduction; geometrical vectors [175] --
5.2 General vector spaces [181] --
5.3 Linear dependence and linear independence [187] --
5.4 Basis, dimension, and coordinates [195] --
5.5 Bases and matrices [207] --
5.6 Length and distance in vector spaces: norms [275] --
5.7 Angle in vector spaces: inner products [220] --
5.8 Orthogonal projections and bases: general spaces and Gram-Schmidt [226] --
5.9 Orthogonal projections and bases: Rp, Cp, QR, and least squares [234] --
5.10 Miscellaneous problems [246] --
Chapter 6: LINEAR TRANSFORMATIONS AND MATRICES [249] --
6.1 Introduction; linear transformations [249] --
6.2 Matrix representations of linear transformations [257] --
6.3 Norms of linear transformations and matrices [263] --
6.4 Inverses of perturbed matrices; condition of linear equations [268] --
6.5 Miscellaneous problems [277] --
Chapter 7: EIGENVALUES AND EIGENVECTORS: AN OVERVIEW [279] --
7.1 Introduction [279] --
7.2 Definitions and basic properties [284] --
7.3 Eigensystems, decompositions, and transformation representations [293] --
7.4 Similarity transformations; Jordan form [299] --
7.5 Unitary matrices and unitary similarity; Schur and diagonal forms [304] --
7.6 Computer software for finding eigensystems [315] --
7.7 Condition of eigensystems [317] --
7.8 Miscellaneous problems [322] --
Chapter 8: EIGENSYSTEMS OF SYMMETRIC, HERMITIAN, AND NORMAL MATRICES, WITH APPLICATIONS [325] --
8.1 Introduction [325] --
8.2 Schur form and decomposition; normal matrices [326] --
8.3 Eigensystems of normal matrices [331] --
8.4 Application: singular value decomposition [338] --
8.5 Application: least squares and the pseudoinverse [346] --
8.6 Miscellaneous problems [353] --
Chapter 9: EIGENSYSTEMS OF GENERAL MATRICES, WITH APPLICATIONS [355] --
9.1 Introduction [355] --
9.2 Jordan form [357] --
9.3 Eigensystems for general matrices [364] --
9.4 Application: discrete system evolution and matrix powers [369] --
9.5 Application: continuous system evolution and matrix exponentials [378] --
9.6 Application: iterative solution of linear equations [388] --
9.7 Miscellaneous problems [395] --
Chapter 10: QUADRATIC FORMS AND VARIATIONAL CHARACTERIZATIONS OF EIGENVALUES [398] --
10.1 Introduction [398] --
10.2 Quadratic forms in R2 [400] --
10.3 Quadratic forms in Rp and Cp [407] --
10.4 Extremizing quadratic forms: Rayleigh’s principle [415] --
10.5 Extremizing quadratic forms: the min-max principle [423] --
10.6 Miscellaneous problems [428] --
Chapter 11: --
LINEAR PROGRAMMING [433] --
11.1 Analysis of a simple example [433] --
11.2 A general linear program [448] --
11.3 Solving a general linear program [454] --
11.4 Duality [465] --
11.5 Miscellaneous problems [475] --
Appendix 1: --
ANSWERS AND AIDS TO SELECTED PROBLEMS [479] --
Appendix 2: --
BIBLIOGRAPHY [502] --
INDEX OF NOTATION [505] --
SUBJECT INDEX [509] --
MR, 58 #28016
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