Category Archives: Fall 2019

On the semiscalar equivalence of 3-by-3 matrices with all different characteristic roots

 

Bogdan Shavarovskii

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

October 15, 2019 at 15:05 in Lecture Room 377

Abstract of talk

Some invariants of 3-by-3 polynomial matrices with all different characteristic roots are found. In some cases, the conditions of semiscalar equivalence of such matrices are specified and canonical forms are constructed.

Equivalence of matrices over quadratic rings and matrix equations

 

Natalija Ladzoryshyn

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

September 24, 2019 at 15:05 in Lecture Room 377

Abstract of talk

The notation of the (z,k)-equivalence of matrices over quadratic rings is introduced. The standard forms of matrices and their pairs with respect to this equivalence are established. The conditions of solvability of matrix linear unilateral and bilateral equations over an arbitrary quadratic ring are given and their integer solutions are described. On the basis of constructed standard forms of matrices, we proposed the effective method of solvability of these matrix equations and description of the structure of their solutions.