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.
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 
-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.
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.
Nataliia Dzhaliuk
March 12, 2019
The arithmetic of solutions of the equation A = BX
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Volodymyr ShchedrykDepartment of Algebra, Pidstryhach |
February 26, 2019 at 15:05 in Lecture Room 377 |
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Abstract of talk
We describing the properties of g.c.d. and l.c.m. of matrix equation 
solutions over
commutative elementary divisor domain.
February 26, 2019
Elementary reduction of matrices over rings with almost stable range 1
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Bohdan ZabavskyDepartment of Algebra and Logic |
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Andriy RomanivDepartment of Algebra, Pidstryhach |
November 27, 2018 at 15:05 in Lecture Room 377 |
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Abstract of talk
In the talk we investigate the elementary reduction of matrices over rings with almost stable range 1.
Andriy Romaniv
November 27, 2018
Classification of Symmetry Reductions for the Eikonal Equation
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Vasyl’FedorchukInstitute of Mathematics, |
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Volodymyr FedorchukDepartment of Algebra, |
November 6, 2018 at 15:05 in Lecture Room 377 |
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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.
Volodymyr Fedorchuk
November 6, 2018
Reduced Triangular Form of Polynomial Matrices and Its Invariants
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Bogdan ShavarovskiiDepartment of Algebra, Pidstryhach |
October 16, 2018 at 15:05 in Lecture Room 377 |
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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.
October 16, 2018
Session dedicated to the memory of professor Vasyl’ Ivanovych Andriychuk
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Session of the Lviv Algebraic Seminar dedicated to the memory of professorVasyl’ Ivanovych Andriychuk |
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September 18, 2018 at 15:00 in Lecture Room 377 |
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