33 citations · 123 across the 18 of their papers we have counts for
10 papers · 1 filter
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 complex matrices under transformations , and , w…
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…
Even grade generic skew-symmetric matrix polynomials with bounded rank
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
We show that the set of complex skew-symmetric matrix polynomials of even grade , i.e., of degree at most , and (normal) rank at most is the closure of the…
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…
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…
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…
Miniversal deformations of pairs of symmetric matrices under congruence
Andrii Dmytryshyn
For each pair of complex symmetric matrices we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices $(\wi…
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 we provide a normal form with a minimal n…
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 and for the closure ordering on the sets of congruence classes of and complex matrices. In other words, we const…
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…