V. Sergeichuk

activity

20072020

most citedCanonical matrices for linear matrix problems

94 citations · 912 across the 61 of their papers we have counts for

collaborators

Showing 2016 · math.RAShow all

3 papers · 2 filters

math.RA2016★ 41 cited

Roth's solvability criteria for the matrix equations $A X - X B = C$ and $X - A X B = C$ over the skew field of quaternions with an involutive automorphism $q \mapsto q^$

Vyacheslav Futorny, Tetiana Klymchuk, Vladimir V. Sergeichuk

The matrix equation $A X - X B = C$ has a solution if and only if the matrices [A&C\\0&B] and [A &0\\0 & B] are similar. This criterion was proved over a field by W.E. Roth (1952) and ov…

math.RA2016★ 6 cited

Neighborhood radius estimation for Arnold's miniversal deformations of complex and $p$ -adic matrices

Victor A. Bovdi, Mohammed A. Salim, Vladimir V. Sergeichuk

V.I. Arnold (1971) constructed a simple normal form to which all complex matrices $B$ in a neighborhood $U$ of a given square matrix $A$ can be reduced by similarity transformation…

math.RA2016★ 3 cited

Each n-by-n matrix with n>1 is a sum of 5 coninvolutory matrices

Ma. Nerissa M. Abara, Dennis I. Merino, Vyacheslav I. Rabanovich +2

An $n \times n$ complex matrix $A$ is called coninvolutory if $A ˉ A = I_{n}$ and skew-coninvolutory if $A ˉ A = - I_{n}$ (which implies that $n$ is even). We prove that each matrix of s…

Roth's solvability criteria for the matrix equations AX−XB=C and X−AXB=C over the skew field of quaternions with an involutive automorphism q↦q^​

Neighborhood radius estimation for Arnold's miniversal deformations of complex and p-adic matrices

Each n-by-n matrix with n>1 is a sum of 5 coninvolutory matrices

Roth's solvability criteria for the matrix equations $A X - X B = C$ and $X - A X B = C$ over the skew field of quaternions with an involutive automorphism $q \mapsto q^$

Neighborhood radius estimation for Arnold's miniversal deformations of complex and $p$ -adic matrices