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Introduction to Linear Algebra
ISBN: 9780201824162 | 0201824167
Format: HardcoverPublisher: Pearson College Div
Pub. Date: 8/1/1997
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This book stresses both practical computation and theoretical principles and centers on the early introduction of matrix theory and systems of linear equations, elementary vector-space concepts, and the eigenvalue problem. Featuring a gradual increase in the level of difficulty, an accessible writing style, and the integration of MATLAB, this text is an excellent introduction for engineering students.
| Matrices and Systems of Linear Equations | |
| Introduction to Matrices and Systems of Linear Equations | |
| Echelon Form and Gauss-Jordan Elimination | |
| Consistent Systems of Linear Equations | |
| Applications (Optional) | |
| Matrix Operations | |
| Algebraic Properties of Matrix Operations | |
| Linear Independence and Nonsingular Matrices | |
| Data Fitting, Numer... MORE | |
| Matrix Inverses and Their Properties | |
| Vectors in 2-Space and 3-Space | |
| Vectors in the Plane | |
| Vectors in Space | |
| The Dot Product and the Cross Product | |
| Lines and Planes in Space | |
| The Vector Space Rn | |
| Introduction | |
| Vector Space Properties of Rn | |
| Examples of Subspaces | |
| Bases for Subspaces | |
| Dimension | |
| Orthogonal Bases for Subspaces | |
| Linear Transformations from Rn to Rm | |
| Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting | |
| Theory and Practice of Least Squares | |
| The Eigenvalue Problem | |
| The Eigenvalue Problem for (2 x 2) Matrices | |
| Determinants and the Eigenvalue Problem | |
| Elementary Operations and Determinants (Optional) | |
| Eigenvalues and the Characteristic Polynomial | |
| Eigenvectors and Eigenspaces | |
| Complex Eigenvalues and Eigenvectors | |
| Similarity Transformations and Diagonalization | |
| Difference Equations | |
| Markov Chains, Systems of Differential Equations (Optional) | |
| Vector Spaces and Linear Transformations | |
| Introduction | |
| Vector Spaces | |
| Subspaces | |
| Linear Independence, Bases, and Coordinates | |
| Dimension | |
| Inner-Product Spaces, Orthogonal Bases, and Projections (Optional) | |
| Linear Transformations | |
| Operations with Linear Transformations | |
| Matrix Representations for Linear Transformations | |
| Change of Basis and Diagonalization | |
| Determinants | |
| Introduction | |
| Cofactor Expansions of Determinants | |
| Elementary Operations and Determinants | |
| Cramer's Rule | |
| Applications of Determinants: Inverses and Wronksians | |
| Eigenvalues and Applications | |
| Quadratic Forms | |
| Systems of Differential Equations | |
| Transformation to Hessenberg Form | |
| Eigenvalues of Hessenberg Matrices | |
| Householder Transformations | |
| The QR Factorization and Least-Squares Solutions | |
| Matrix Polynomials and the Cayley-Hamilton Theorem | |
| Generalized Eigenvectors and Solutions of Systems of Differential Equations | |
| Appendix: An Introduction to MATLAB | |
| Answers to Selected Odd-Numbered Exercises | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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