Category Archives: Current semester

On adequacy of full matrices over adequate rings

Andrii Gatalevych

Department of Higher Mathematics
Faculty of Mechanics and Mathematics
Ivan Franko
National University of L’viv

Volodymyr Shchedryk

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

November 27, 2020 at 16:00 online

Abstract of talk

The set of full matrices (i.e., matrices whose elements are relatively prime) of the second order over an adequate ring R is investigated. The concept of an adequate element in non-commutative rings is introduced. It is proved that nonsingular full second order matrices are right (left) adequate elements in the ring of second order matrices over R.

AAA

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.

AAA

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.

AAA