94 citations · 912 across the 61 of their papers we have counts for
62 papers
Classification of linear operators satisfying or on a vector space with indefinite scalar product
Victor Senoguchi Borges, Iryna Kashuba, Vladimir V. Sergeichuk +2
We classify all linear operators satisfying and all linear operators satisfying with on a complex, real, or quaternion…
Pairs of commuting nilpotent operators with one-dimensional intersection of kernels and matrices commuting with a Weyr matrix
Vitalij M. Bondarenko, Vyacheslav Futorny, Anatolii P. Petravchuk +1
I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) of commuting nilpotent operators on a vector space contains the problem of classifying an…
Congruence of matrix spaces, matrix tuples, and multilinear maps
Genrich R. Belitskii, Vyacheslav Futorny, Mikhail Muzychuk +1
Two matrix vector spaces are said to be equivalent if for some nonsingular and . These spaces are congruent if . We prove t…
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…
Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form
Jonathan V. Caalim, Vyacheslav Futorny, Vladimir V. Sergeichuk +1
Let be a vector space over a field with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If ,…
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…