T. Klymchuk

activity

20162020

most citedRoth's solvability criteria for the matrix equations

A X - X B = C

and

X - A X B = C

over the skew field of quaternions with an involutive automorphism

q \mapsto q^

41 citations · 105 across the 7 of their papers we have counts for

collaborators

Showing 2017Show all

2 papers · 1 filter

math.RT2017★ 7 cited

Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras

Vyacheslav Futorny, Tetiana Klymchuk, Anatolii P. Petravchuk +1

For each two-dimensional vector space $V$ of commuting $n \times n$ matrices over a field $F$ with at least 3 elements, we denote by $V$ the vector space of all $…

math.RT2017★ 30 cited

Generalization of Roth's solvability criteria to systems of matrix equations

Andrii Dmytryshyn, Vyacheslav Futorny, Tetiana Klymchuk +1

W.E. Roth (1952) proved that the matrix equation $A X - X B = C$ has a solution if and only if the matrices $[A 0 C B]$ and $\left[\begin{matrix}A&0…