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Elementary linear algebra /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Orlando, Fla. :
Academic Press College Division,
�1986.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Elementary Linear Algebra; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction to Linear Equations and Matrices; 1.1 Introduction to Linear Systems and Matrices; 1.2 Gaussian Elimination; 1.3 The Algebra of Matrices; 1.4 Inverses and Elementary Matrices; 1.5 Gaussian Elimination as a Matrix Factorization; 1.6 Transposes, Symmetry, and Band Matrices; An Application; 1.7 Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems; Review Exercises; Chapter 2. Vector Spaces; 2.1 Vectors in 2- and 3-Spaces.
- 2.2 Euclidean n-Space2.3 General Vector Spaces; 2.4 Subspaces, Span, Null Spaces; 2.5 Linear Independence; 2.6 Basis and Dimension; 2.7 The Fundamental Subspaces of a Matrix; Rank; 2.8 An Application: Error-Correcting Codes; Review Exercises; Chapter 3. Linear Transformations, Orthogonal Projections, and Least Squares; 3.1 Matrices as Linear Transformations; 3.2 Relationships Involving Inner Products; 3.3 Least Squares and Orthogonal Projections; 3.4 Orthogonal Bases and the Gram-Schmidt Process; 3.5 Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited).
- 3.6 Encoding the QR Decomposition-A Geometric ApproachReview Exercises; Chapter 4. Eigenvectors and Eigenvalues; 4.1 A Brief Introduction to Determinants; 4.2 Eigenvalues and Eigenvectors; 4.3 Diagonalization; 4.4 Symmetric Matrices; 4.5 An Application-Difference Equations: Fibonacci Sequences and Markov Processes; 4.6 An Application-Differential Equations; 4.7 An Application-Quadratic Forms; 4.8 Solving the Eigenvalue Problem Numerically; Review Exercises; Chapter 5. Determinants; 5.1 The Determinant Function; 5.2 Evaluating Determinants; 5.3 Properties of Determinants.
- 5.4 Cofactor Expansion Cramer's Rule; Review Exercises; Chapter 6. Further Directions; 6.1 Function Spaces; 6.2 Singular Value Decomposition and Generalized Inverses; 6.3 General Vector Spaces and Linear Transformations Over an Arbitrary Field; Review Exercises; Appendices; Appendix A: More on LU Decompositions; Appendix B: Counting Operations and Gauss-Jordan Elimination; Appendix C: Another Application; Appendix D: Software and Codes for Linear Algebra; Bibliography and Further Readings; Answers to Odd-Numbered Exercises; Index.