Forskningsseminarium: Tillämpad linjär algebra – matrisekvationer och faktorisering
Välkommen till forskningsseminarium Tillämpad linjär algebra: matrisekvationer och faktorisering!
Plats: D207 och via Zoom. Anslut till zoomrummet här!
Talare: Andrii Dmytryshyn, Mathematics, School of Science and Technology, Örebro University
Seminariet kommer att hållas på engelska. Ingen anmälan krävs.
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.