Applied linear algebra: matrix equations and factorizations
Welcome to the research seminar Applied linear algebra: matrix equations and factorizations!
Speaker: Andrii Dmytryshyn, Mathematics, School of Science and Technology, Örebro University
Location: Room D207, and on Zoom via link https://hb-se.zoom.us/j/68280905608
This seminar will be held in English. Open seminar, no registration required.
About the seminar
I will present an overview of our research on two classical topics in Matrix Analysis and Applied Linear Algebra, namely challenging problems regarding the solution matrix equations and the analysis of the complete eigenstructure of matrices under perturbations. Then I will focus on our results about coupled matrix equations and block diagonalization:
In 1952 Roth revealed the connection between the existence of a solution (i.e., the consistency) for a Sylvester matrix equation AX-XB=C and the similarity (having the same eigenvalues and their multiplicities) of the particular block-matrices constructed from the matrix coefficients of the considered Sylvester matrix equation. Since then, similar results have been published for a number of other Sylvester-type matrix equations as well as for some systems of matrix equations. I will present the general Roth’s type theorem for systems of matrix equations consisting of an arbitrary mix of Sylvester-type equations.