A tantárgyleírás hatályossága
| Subject name (Hungarian, English) |
Mátrixanalízis
Analysis of Matrices
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| Subject code | BMEVIMAD569 | ||||||||||||
| Subject type | — | ||||||||||||
| Training Level | — | ||||||||||||
| Course types and hours (weekly/semester) |
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| Assessment type | vizsga | ||||||||||||
| Credits | 5 | ||||||||||||
| Subject coordinator |
Pach Péter Pál
contact:
pach.peter@vik.bme.hu
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| Responsible department |
Gépjárműtechnológia Tanszék
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| Faculty | Közlekedésmérnöki és Járműmérnöki Kar | ||||||||||||
| Subject website | http://cs.bme.hu/~ppp/ma/index-en.html | ||||||||||||
| Primary curriculum type | — | ||||||||||||
| Direct prerequisites – Strong prerequisite | none | ||||||||||||
| Direct prerequisites – Weak prerequisite | none | ||||||||||||
| Direct prerequisites – Parallel prerequisite | none | ||||||||||||
| Direct prerequisites – Milestone prerequisite | none | ||||||||||||
| Direct prerequisites – Exclusion | none |
Objectives
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
Learning outcomes
Ez a tantárgy a KKK rendeletben meghatározott, következő kompetenciák fejlesztését szolgálja:
Knowledge
No learning outcomes recorded.
Skills
No learning outcomes recorded.
Attitudes
No learning outcomes recorded.
Autonomy and responsibility
No learning outcomes recorded.
Oktatási módszertan
Tanulástámogató anyagok
Online források
Recommended preliminary knowledge for completing the subject
General rules
Assessment methods
In-term assessments
No detailed assessments provided.
Weight of in-term assessments
No weights provided.
Exam-period assessments
No detailed assessments provided.
Weight of exam elements
No weights provided.
Grade calculation
No grade thresholds provided.
Attendance requirements
No attendance requirements provided.
Rules for retake and resubmission
Not provided.
Short description
Not provided.
Detailed description
Not provided.
Recommended courses
Workload to complete the subject
No workload breakdown provided.
Validity of subject requirements
Curriculum placement
No curriculum placements recorded for this subject version.