41 citations · 105 across the 7 of their papers we have counts for
7 papers
Operators on positive semidefinite inner product spaces
Victor A. Bovdi, Tetiana Klymchuk, Tetiana Rybalkina +2
We give canonical forms of selfadjoint and isometric operators on a complex vector space with scalar product given by a positive semidefinite Hermitian form, and of Hermitian f…
A constructive proof of Pokrzywa's theorem about perturbations of matrix pencils
Vyacheslav Futorny, Tetiana Klymchuk, Vladimir V. Sergeichuk +1
Our purpose is to give new proofs of several known results about perturbations of matrix pencils. Andrzej Pokrzywa (1986) described the closure of orbit of a Kronecker canonical pe…
Perturbation analysis of a matrix differential equation
M. Isabel Garcìa-Planas, Tetiana Klymchuk
Two complex matrix pairs and are contragrediently equivalent if there are nonsingular and such that . M.I. Garc\'ıa-Planas an…
Regularizing algorithm for mixed matrix pencils
Tetiana Klymchuk
P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker's canonical form of a matrix pencil. His algorithm uses only unitary transformations,…
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 of commuting matrices over a field with at least 3 elements, we denote by the vector space of all $…
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 has a solution if and only if the matrices and $\left[\begin{matrix}A&0…
Roth's solvability criteria for the matrix equations and over the skew field of quaternions with an involutive automorphism
Vyacheslav Futorny, Tetiana Klymchuk, Vladimir V. Sergeichuk
The matrix equation has a solution if and only if the matrices [A&C\\0&B] and [A &0\\0 & B] are similar. This criterion was proved over a field by W.E. Roth (1952) and ov…