Matrix Methods : An Introduction
This new edition of "Matrix Methods" emphasizes applications to Jordan-canonical forms, differential equations, and least squares. The revision now includes an entire new chapter on inner products, additional material on elementary row applications, and hundreds of new exercises. It provides an introduction to the functional approach to programming. It emphasizes the problem to be solved, not the programming language. It takes the view that all computer programs are a definition of a function. It includes exercises for each chapter. It requires at least a high school algebra level of mathematical sophistication. It is a self-contained work. It can be used as a pre-programming language introduction to the mathematics of computing.
- Hardback | 503 pages
- 198 x 236 x 32mm | 1,061.4g
- 23 Apr 1991
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
- 2nd Revised edition
Table of contents
Matrices. Basic Concepts. Operations. Matrix Multiplication. Special Matrices. Submatrices and Partitioning. Vectors. The Geometry of Vectors. Simultaneous Linear Equations: Linear Systems. Solutions by Substitution. Gaussian Elimination. Pivoting Strategies. Linear Independence. Rank. Theory of Solutions. Appendix. The Inverse: Introduction. Calculating Inverses. Simultaneous Equations. Properties of the Inverse. LU Decomposition. Appendix. Determinants. Expansion by Confactors. Properties of Determinants. Pivotal Condensation. Inversion. Cramer's Rule. Appendix. Eigenvalues and Eigenvectors. Definitions. Eigenvalues. Eigenvectors. Properties of Eigenvalues and Eigenvectors. Linearly Independent Eigenvectors. Power Methods. Real Inner Products. Introduction. Orthonormal Vectors. Projections and QR Decompostions. The QR Algorithm. Least*b1Squares. Matrix Calculus. Well-Defined Functions. Cayley-Hamilton Theorem. Polynomials of Matrices--Distinct Eigenvalues. Polynomials of Matrices--General Case. Fuctions of a Matrix. The Function eAt. Complex Eigenvalues. Properties of eA. Derivatives of a Matrix. Appendix. Linear Differential Equations. Fundamental Form. Reduction of an nth Order Equation. Reduction of a System. Solutions of Systems with Constant Coefficients. Solutions of Systems--General Case. Appendix. Jordan Canonical Forms. Similar Matrices. Diagonalizable Matrices. Functions of Matrices--Diagonalizable Matrices. Generalized Eigenvectors. Chains. Canonical Basis. Jordan Canonical Forms. Functions of Matrices--General Case. The Function eAt. Appendix. Special Matrices. Complex Inner Product. Self-Adjoint Matrices. Real Symmetric Matrices. Orthogonal Matrices. Hermitian Matrices. Unitary Matrices. Summary. Positive Definite Matrices. Answers and Hints to Selected Problems. Index.