29 citations · 35 across the 4 of their papers we have counts for
5 papers
An informal introduction to perturbations of matrices determined up to similarity or congruence
Lena Klimenko, Vladimir V. Sergeichuk
The reductions of a square complex matrix A to its canonical forms under transformations of similarity, congruence, or *congruence are unstable operations: these canonical forms an…
A holomorphic transformation to a miniversal deformation under *congruence does not always exist
Lena Klimenko
V.I. Arnold [Russian Math. Surveys 26(2) (1971) 29-43] constructed miniversal deformations of square complex matrices under similarity. Reduction transformations to them and also t…
Change of the *congruence canonical form of 2-by-2 matrices under perturbations
Vyacheslav Futorny, Lena Klimenko, Vladimir V. Sergeichuk
We study how small perturbations of a 2-by-2 complex matrix can change its canonical form for *congruence. We construct the Hasse diagram for the closure ordering on the set of *co…
Block triangular miniversal deformations of matrices and matrix pencils
Lena Klimenko, Vladimir V. Sergeichuk
For each square complex matrix, V. I. Arnold constructed a normal form with the minimal number of parameters to which a family of all matrices B that are close enough to this matri…
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…