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Methods of matrix algebra /
Methods of matrix algebra.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1965.
|
| Colección: | Mathematics in science and engineering ;
v. 16. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Methods of Matrix Algebra; Copyright Page; Contents; Foreword; Symbols and Conventions; Chapter I. Vectors and Matrices; 1. Vectors; 2. Addition of Vectors and Scalar Multiplication; 3. Linear Vector Spaces; 4. Dimensionality and Bases; 5. Linear Homogeneous Systems-Matrices; 6. Partitioned Matrices; 7. Addition of Matrices and Scalar Multiplication; 8. Multiplication of a Matrix Times a Vector; 9. Matrix Multiplication; 10. An Algebra; 11. Commutativity; 12. Divisors of Zero; 13. A Matrix as a Representation of an Abstract Operator; 14. Other Product Relations
- 15. The Inverse of a Matrix16. Rank of a Matrix; 17. Gauss's Algorithm; 18. 2-Port Networks; 19. Example; Chapter II. The Inner Product; 1. Unitary Inner Product; 2. Alternative Representation of Unitary Inner Product; 3. General (Proper) Inner Product; 4. Euclidean Inner Product; 5. Skew Axes; 6. Orthogonality; 7. Normalization; 8. Gram-Schmidt Process; 9. The Norm of a Vector; Chapter III. Eigenvalues and Eigenvectors; 1. Basic Concept; 2. Characteristic or Iterative Impedance; 3. Formal Development; 4. Determination of the Eigenvalues; 5. Singularity; 6. Linear Independence
- 7. Semisimplicity8. Nonsemisimple Matrices; 9. Degeneracy in a Chain; 10. Examples; 11. p-Section of a Filter; 12. Structure of the Characteristic Equation; 13. Rank of a Matrix; 14. The Trace of a Matrix; 15. Reciprocal Vectors; 16. Reciprocal Eigenvectors; 17. Reciprocal Generalized Eigenvectors; 18. Variational Description of the Eigenvectors and Eigenvalues; Chapter IV. Hermitian, Unitary, and Normal Matrices; 1. Adjoint Relation; 2. Rule of Combination; 3. The Basic Types; 4. Decomposition into Hermitian Components; 5. Polar Decomposition; 6. Structure of Normal Matrices
- 7. The Converse Theorem8. Hermitian Matrices; 9. Unitary Matrices; 10. General (Proper) Inner Product; Chapter V. Change of Basis, Diagonalization, and the Jordan Canonical Form; 1. Change of Basis and Similarity Transformations; 2. Equivalence Transformations; 3. Congruent and Conjunctive Transformations; 4. Example; 5. Gauge Invariance; 6. Invariance of the Eigenvalues under a Change of Basis; 7. Invariance of the Trace; 8. Variation of the Eigenvalues under a Conjunctive Transformation; 9. Diagonalization; 10. Diagonalization of Normal Matrices
- 11. Conjunctive Transformation of a Hermitian Matrix12. Example; 13. Positive Definite Hermitian Forms; 14. Lagrange's Method; 15. Canonical Form of a Nonsemisimple Matrix; 16. Example; 17. Powers and Polynomials of a Matrix; 18. The Cayley-Hamilton Theorem; 19. The Minimum Polynomiail; 20. Examples; 21. Summary; Chapter VI. Functions of a Matrix; 1. Differential Equations; 2. Reduction of Degree; 3. Series Expansion; 4. Transmission Line; 5. Square Root Function; 6. Unitary Matrices as Exponentials; 7. Eigenvectors; 8. Spectrum of a Matrix; 9. Example; 10. Commutativity