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Matrix methods an introduction.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York,
Academic Press
[�1969]
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Methods: An Introduction; Copyright Page; Table of Contents; Preface; Acknowledgments; CHAPTER 1. MATRICES; 1.1 Matrices; 1.2 Operations; 1.3 Matrix Multiplication-I; 1.4 Matrix Multiplication-II; 1.5 Special Matrices; 1.6 Submatrices and Partitioning; 1.7 Vectors; CHAPTER 2. DETERMINANTS; 2.1 Determinants; 2.2 Expansion by Cofactors; 2.3 Properties of Determinants; 2.4 Pivotal Condensation; 2.5 Cramer's Rule; CHAPTER 3. THE INVERSE; 3.1 The Inverse; 3.2 Simultaneous Equations; 3.3 Properties of the Inverse; 3.4 Another Method for Inversion; Appendix to Chapter 3
- CHAPTER 4. SIMULTANEOUS LINEAR EQUATIONS4.1 Linear Systems; 4.2 Solutions by Inversion; 4.3 Gaussian Elimination; 4.4 Linear Independence; 4.5 Rank; 4.6 Theory of Solutions; 4.7 Matrix Solutions; 4.8 Homogeneous Systems; CHAPTER 5. EIGENVALUES AND EIGENVECTORS; 5.1 Definitions; 5.2 Eigenvalues; 5.3 Eigenvectors; 5.4 Properties of Eigenvalues and Eigenvectors; 5.5 Linearly Independent Eigenvectors; CHAPTER 6. MATRIX CALCULUS; 6.1 Definitions; 6.2 Cayley-Hamilton Theorem; 6.3 Polynomials of Matrices-Distinct Eigenvalues; 6.4 Polynomials of Matrices-General Case; 6.5 Functions of a Matrix
- 6.6 The Function eAt6.7 Complex Eigenvalues; 6.8 Properties of eA; 6.9 Derivatives of a Matrix; Appendix to Chapter 6; CHAPTER 7. LINEAR DIFFERENTIAL EQUATIONS; 7.1 Fundamental Form; 7.2 Reduction of an nth Order Equation; 7.3 Reduction of a System; 7.4 Solutions of Systems with Constant Coefficients; 7.5 Examples; 7.6 Solutions of Systems-General Case; 7.7 Properties of the Transition Matrix; 7.8 The Adjoint System; Appendix to Chapter 7; CHAPTER 8. JORDAN CANONICAL FORMS; 8.1 Similar Matrices; 8.2 Diagonalizable Matrices; 8.3 Functions of Matrices-Diagonalizable Matrices
- 8.4 Generalized Eigenvectors8.5 Chains; 8.6 Canonical Basis; 8.7 Jordan Canonical Forms; 8.8 Functions of Matrices-General Case; 8.9 The Function eAt; Appendix to Chapter 8; CHAPTER 9. SPECIAL MATRICES; 9.1 Introduction; 9.2 Inner Products; 9.3 Orthonormal Vectors; 9.4 Self-Adjoint Matrices; 9.5 Real Symmetric Matrices; 9.6 Orthogonal Matrices; 9.7 Hermitian Matrices; 9.8 Unitary Matrices; 9.9 Summary; 9.10 Positive Definite Matrices; ANSWERS AND HINTS TO SELECTED PROBLEMS; References; Index