Analysis of Matrices
A tantárgy neve magyarul / Name of the subject in Hungarian: Mátrixanalízis
Last updated: 2021. március 12.
Dr. Friedl Katalin
associate professor
Department of Computer Science and Information Theory
Dr. Pach Péter Pál
1. Special matrix products; Rank One Decomposition, linear combination of rank-one matrices
2. Matrix inversion
3. Rank of a matrix, minimal rank-one decomposition
4. Rank theorems, equivalent transformations
5. Sylvester’s law of nullity
6. Special matrices and their inverse
7. Inverse of a modified matrix
8. Projections, theorems about projections
9. Generalized inverse
10. Theory of systems of linear equations and their solution
11. Systems of linear equations with a quadratic coefficient matrix
12. Linear transformations; bilinear and quadratic forms
13. The eigenvalue problem of matrices
14. Diagonalizable transformations; Hermitian and unitary transformations
15. Spectral decomposition of matrices; unitarily diagonalizable matrices
16. Cayley - Hamilton theorem and its refinement
17. Matrix functions and reduction to matrix polynomials
18. (Matrix-valued) Lagrange-polynomials and their properties
19. Determining the Lagrange matrix polynomials with the help of the adjugate of the characteristic matrix
20. Calculating matrix functions with Hermite matrix polynomials; non-diagonalizable matrices
21. Properties of the Hermite matrix polynomials
22. Transforming nilpotent matrices into Jordan normal form
23. Canonical form of functions of nilpotent matrices
24. Canonical form of matrix functions
25. Theory of elementary divisors
26. Application of matrix functions in the theory of systems of linear differential equations
27. Solving linear systems of differential equations
Signature: 1 homework.
Final: oral exam.
Rózsa Pál: Lineáris algebra és alkalmazásai. 3. átdolgozott kiadás. Tankönyvkiadó, Budapest, 1991.
H. Golub – C.F. Van Loan: Matrix Computations, The John Hopkins University Press, 1989.