Screen LibraryElementary linear algebra /
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
Academic Press College Division,
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| Publisher Address: | Orlando, Fla. : |
| Publication Dates: | 1986. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780123484604 |
| Carrier Form: | 1 online resource (ix, 404 pages) : illustrations (some color) |
| Bibliography: | Includes bibliographical references (pages 377-378) and index. |
| ISBN: |
9781483265179 148326517X |
| Index Number: | QA184 |
| CLC: | O151.2 |
| Contents: |
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. |