Andrii Dmytryshyn

activity

20102026

most citedMiniversal deformations of matrices of bilinear forms

33 citations · 123 across the 18 of their papers we have counts for

collaborators

20 papers

math.NA2026

Distance to nearest skew-symmetric matrix polynomials of bounded rank

Andrii Dmytryshyn, Froilán M. Dopico, Rakel Hellberg

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$ . The algori…

math.RT2025

Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces

Sweta Das, Andrii Dmytryshyn, Volker Mehrmann

We derive the canonical forms for a pair of $n \times n$ complex matrices $(E, Q)$ under transformations $(E, Q) \to (U E V, U^{- T} Q V)$ , and $(E, Q) \to (U E V, U^{-*} Q V)$ , w…

math.RT2025

Minimal degenerations of orbits of skew-symmetric matrix pencils

Sweta Das, Andrii Dmytryshyn

Complete eigenstructure, e.g., eigenvalues with multiplicities and minimal indices, of a skew-symmetric matrix pencil may change drastically if the matrix coefficients of the penci…

math.RT2023

Even grade generic skew-symmetric matrix polynomials with bounded rank

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We show that the set of $m \times m$ complex skew-symmetric matrix polynomials of even grade $d$ , i.e., of degree at most $d$ , and (normal) rank at most $2 r$ is the closure of the…

math.RT2023

Versal deformations: A tool of linear algebra

Andrii Dmytryshyn

Versal deformation of a matrix A is a normal form to which all matrices A + E, close to A, can be reduced by similarity transformation smoothly depending on the entries of A + E. I…

math.NA2023

Minimal rank factorizations of polynomial matrices

Andrii Dmytryshyn, Froilán Dopico, Paul Van Dooren

We investigate rank revealing factorizations of $m \times n$ polynomial matrices $P (λ)$ into products of three, $P (λ) = L (λ) E (λ) R (λ)$ , or two, $P (λ) = L (λ) R (λ)$ , polynomial matr…

math-ph2023★ 2 cited

Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges

F Rousse, M Fasi, A Dmytryshyn +2

The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical…

math.NA2022

Generic eigenstructures of Hermitian pencils

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We obtain the generic complete eigenstructures of complex Hermitian $n \times n$ matrix pencils with rank at most $r$ (with $r \leq n$ ). To do this, we prove that the set of such pen…

math.NA2020

Recovering a perturbation of a matrix polynomial from a perturbation of its linearization

Andrii Dmytryshyn

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need t…

math.CO2020★ 1 cited

Schur decomposition of several matrices

Andrii Dmytryshyn

Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequ…

math.NA2019

Generic symmetric matrix polynomials with bounded rank and fixed odd grade

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We determine the generic complete eigenstructures for $n \times n$ complex symmetric matrix polynomials of odd grade $d$ and rank at most $r$ . More precisely, we show that the set…

math.SP2018

Generic symmetric matrix pencils with bounded rank

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We show that the set of $n \times n$ complex symmetric matrix pencils of rank at most $r$ is the union of the closures of $⌊ r /2 ⌋ + 1$ sets of matrix pencils with some,…

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…

math.RA2017

Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade

Andrii Dmytryshyn, Froilan M. Dopico

We show that the set of $m \times m$ complex skew-symmetric matrix polynomials of odd grade $d$ , i.e., of degree at most $d$ , and (normal) rank at most $2 r$ is the closure of the s…

math.NA2016★ 2 cited

Generic matrix polynomials with fixed rank and fixed degree

Andrii Dmytryshyn, Froilán M. Dopico

The set $P_{r, d}^{m \times n}$ of $m \times n$ complex matrix polynomials of grade $d$ and (normal) rank at most $r$ in a complex $(d + 1) mn$ dimensional space is studied. For…

math.RT2011★ 26 cited

Miniversal deformations of matrices under *congruence and reducing transformations

A. Dmytryshyn, V. Futorny, V. V. Sergeichuk

V.I. Arnold [Russian Math. Surveys 26(2) (1971) 29-43] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not…

math.RT2011

Miniversal deformations of pairs of symmetric matrices under congruence

Andrii Dmytryshyn

For each pair of complex symmetric matrices $(A, B)$ we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices $(\wi…

math.RT2011

Miniversal deformations of pairs of skew-symmetric matrices under congruence

Andrii Dmytryshyn

Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair $(A, B)$ we provide a normal form with a minimal n…

math.RT2010★ 29 cited

Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence

Andrii Dmytryshyn, Vyacheslav Futorny, Bo Kågström +2

We construct the Hasse diagrams $G_{2}$ and $G_{3}$ for the closure ordering on the sets of congruence classes of $2 \times 2$ and $3 \times 3$ complex matrices. In other words, we const…

math.RT2010★ 33 cited

Miniversal deformations of matrices of bilinear forms

Andrii R. Dmytryshyn, Vyacheslav Futorny, Vladimir V. Sergeichuk

V.I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a miniversal deformation of matrices under similarity; that is, a simple normal form to which not only a given s…