Home – Home – Jornals – Numerical Analysis and Applications 2023 number 2

The relation between complex matrices H and A, given by the equality H A = ĀH is called the pseudo-commutation. The set S_H of all A that pseudo-commute with a nonsingular n × n matrix H is called the pseudo-commutation class defined by H . Every class S_H is a subspace of the space M_n(C) interpreted as a real vector space of dimension 2n². Under the assumption dim_R S_H = n², we find a necessary and sufficient condition for the possibility to decomplexify all the matrices in S_H by one and the same similarity transformation.