Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Analysis of Matrices

    A tantárgy neve magyarul / Name of the subject in Hungarian: Mátrixanalízis

    Last updated: 2021. március 12.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Course ID Semester Assessment Credit Tantárgyfélév
    VIMAD569 tavasz 4/0/0/v 5 1/1
    3. Course coordinator and department Dr. Pach Péter Pál,
    Web page of the course http://cs.bme.hu/~ppp/ma/index-en.html
    4. Instructors

    Dr. Friedl Katalin

    associate professor

    Department of Computer Science and Information Theory

    Dr. Pach Péter Pál

    associate professor

    Department of Computer Science and Information Theory

    5. Required knowledge Linear algebra, mathematical analysis.
    6. Pre-requisites
    Ajánlott:
    None.
    7. Objectives, learning outcomes and obtained knowledge The students get a deeper insight into the theory of linear algebra. There will be a special emphasis on matrix functions, Jordan normal form, and their application for solving systems of differential equations. This way we would like to deepen the student’s knowledge and understanding according to the demands of other subjects.
    8. Synopsis

     

    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

    9. Method of instruction 4 hours of lecture per week.
    10. Assessment

    Signature: 1 homework.

    Final: oral exam.

    12. Consultations In office hours or by appointment.
    13. References, textbooks and resources

    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.

    14. Required learning hours and assignment
    Kontakt óra56
    Félévközi készülés órákra28
    Felkészülés zárthelyire0
    Házi feladat elkészítése16
    Kijelölt írásos tananyag elsajátítása10
    Vizsgafelkészülés40
    Összesen150
    15. Syllabus prepared by Dr. Rózsa Pál, professor, Department of Computer Science and Information Theory