94 citations · 912 across the 61 of their papers we have counts for
6 papers · 2 filters
Reduction of a pair of skew-symmetric matrices to its canonical form under congruence
V. A. Bovdi, T. G. Gerasimova, M. A. Salim +1
Let be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum \[ (\underline{\underline A},\underline{\und…
Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence
Victor A. Bovdi, Roger A. Horn, Mohamed A. Salim +1
Let be a field of characteristic not , and let be a pair of matrices over , in which is symmetric and is skew-symmetric. A can…
Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras
Vyacheslav Futorny, Tetiana Klymchuk, Anatolii P. Petravchuk +1
For each two-dimensional vector space of commuting matrices over a field with at least 3 elements, we denote by the vector space of all $…
Classification of linear mappings between indefinite inner product spaces
Juan Meleiro, Vladimir V. Sergeichuk, Thiago Solovera +1
Let be a linear mapping between vector spaces and over a field or skew field with symmetric, or skew-symmetric, or Hermitian forms $\mathcal…
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…
Specht's criterion for systems of linear mappings
Vyacheslav Futorny, Roger A. Horn, Vladimir V. Sergeichuk
W.Specht (1940) proved that two complex matrices and are unitarily similar if and only if $\operatorname{trace} w(A,A^{\ast}) = \operatorname{trace} w(B,B^{\ast…