94 citations · 912 across the 61 of their papers we have counts for
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Canonical matrices of forms and pairs of forms over finite and p-adic fields
Vladimir V. Sergeichuk
Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over f…
Criterion of unitary similarity for upper triangular matrices in general position
Douglas Farenick, Vyacheslav Futorny, Tatiana G. Gerasimova +2
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i…
Matrices that are self-congruent only via matrices of determinant one
Tatyana G. Gerasimova, Roger A. Horn, Vladimir V. Sergeichuk
Docovic and Szechtman, [Proc. Amer. Math. Soc. 133 (2005) 2853-2863] considered a vector space V endowed with a bilinear form. They proved that all isometries of V over a field F o…
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…
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…