Subject description - A8B01AMA
Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions
Possible extenstions:
LU factorization, numerical stability of GEM, least squares.
| A8B01AMA | Advanced Matrix Analysis | ||
|---|---|---|---|
| Roles: | P | Extent of teaching: | 3P+1S |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Velebil J. | Completion: | Z,ZK |
| Lecturers: | Křepela M., Rondoš J. | Credits: | 4 |
| Tutors: | Křepela M., Rondoš J. | Semester: | L |
Anotation:
The course covers advanced topics of linear algebra, in particular matrix factorizations and construction of matrix functions.Course outlines:
Main topics:| 1. | Inner product, norm, norm equivalence in finite-dimenstional spaces. | |
| 2. | Projectors and othogonal projectors, Gram-Schmidt orthogonalization method, QR factorization. | |
| 3. | Unitary and orthogonal matrices, Householder reduction. | |
| 4. | Singular value decompostition. | |
| 5. | Eigenvalues, eigenvectors and eigenspaces, diagonalization, Cholesky factorization. | |
| 6. | Schur decomposition, normal and Hermitian matrices. | |
| 7. | Matrix index, nilpotent matrices. | |
| 8. | Jordan form of a matrix, spectral projectors. | |
| 9. | Construction of a matrix function by power series and through the spectral decomposition theorem. | |
| 10. | Matrix functions as Hermite polynomials, Vandermonde system. | |
| 11. | Matrix exponential, solutions to systems of linear ODE with constant coefficients. |
Exercises outline:
Literature:
| 1. | C. D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM 2000 | |
| 2. | M. Dont: Maticová analýza, skripta, nakl. ČVUT 2011 |
Requirements:
Good knowledge of fundamental topics of linear algebra and single-variable analysis is a prerequisity. Some of the course topics need implemenation of multivariable analysis concepts (normed spaces, power series). It is thus recommended to complete a multivariable analysis course (MA2) before registering for this course. Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| BPOES_2020 | Common courses | P | 4 |
| BPOES | Common courses | P | 4 |
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