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

Speaker

BOGDAN SHAVAROVSKII

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

When & where:

October 15, 2019 at 1500  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.

Bogdan Shavarovskii
October 15, 2019

Equivalence of matrices over quadratic rings and matrix equations

Speaker

Natalija Ladzoryshyn

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

When & where:

September 24, 2019 at 1505  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.

Natalija Ladzoryshyn
Septenber 24, 2019

Equivalence and factorization of the Kronecker products of polynomial matrices

Speaker

Volodymyr Zelisko

Department of Algebra and Logic,
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

When & where:

April 16, 2019 at 1505 in Lecture Room 377

Abstract of talk

We consider the problem of equivalence and semiscalar equivalence of the Kronecker products of polynomial matrices and their separation of factors.

Volodymyr Zelisko
April 16, 2019

The structure of block matrices. I. Factorizations in the rings of the block matrices

Speakers

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

When & where

March 12, 2019 at 1500 in Lecture Room 377

Abstract of talk

We investigate equivalences, factorizations, and matrix unilateral and bilateral equations in the rings of the block matrices. In the first part, we consider factorizations of the block matrices, in particular, the block triangular and the block diagonal matrices over integral domains of finitely generated principal ideals. Conditions for existence and uniqueness up to the association of the factorizations in such rings are established.

Vasyl’ Petrychkovych
Nataliia Dzhaliuk

March 12, 2019

The arithmetic of solutions of the equation A = BX

shchedryk_photo

Volodymyr Shchedryk

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

February 26, 2019 at 15:05 in Lecture Room 377

Abstract of talk

We describing the properties of g.c.d. and l.c.m. of matrix equation A = BX solutions over
commutative elementary divisor domain.

Volodymyr Shchedryk
February 26, 2019

Elementary reduction of matrices over rings with almost stable range 1

Bohdan Zabavsky

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

Andriy Romaniv

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

November 27, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In the talk we investigate the elementary reduction of matrices over rings with almost stable range 1.

Bohdan Zabavsky
Andriy Romaniv

November 27, 2018

Classification of Symmetry Reductions for the Eikonal Equation

Vasyl’Fedorchuk

Institute of Mathematics,
Pedagogical University of Kraków, Poland;
Department of Algebra,
Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics
of the NAS of Ukraine

Volodymyr Fedorchuk

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

November 6, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In the talk we present the results concerning the relationship between the structural properties of low-dimensional (dim L ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincare group P(1,4) and the properties of the reduced equations for the eikonal equation. To obtain those results, we have performed the classification of the invariants as well as of the ansatzes for the above mentioned subalgebras. We also present some classes of invariant solutions for the eikonal equation.

Vasyl’ Fedorchuk
Volodymyr Fedorchuk

November 6, 2018

Reduced Triangular Form of Polynomial Matrices and Its Invariants

Bogdan Shavarovskii

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

October 16, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In this report the semiscalar equivalence of polynomial matrices of three-order is
investigated. In particular, the systems of invariants of reduced matrices have been found.

Bogdan Shavarovskii
October 16, 2018

Session dedicated to the memory of professor Vasyl’ Ivanovych Andriychuk 

Session of the Lviv Algebraic Seminar dedicated to the memory of professor 

Vasyl’ Ivanovych Andriychuk 

September 18, 2018 at 15:00 in Lecture Room 377

Program

Photo Gallery

September 18, 2018