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.