On the equivalence of polynomial matrices over a field - Prokip , V. (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 512.64 The polynomial (n× n) matrices A(λ ) and B(λ) over a field F are called semiscalar equivalent if there exists a nonsingular (n× n) matrix P over F and an invertible (n× n) polynomial matrix Q(λ ) over F[λ] such that A(λ ) = PB(λ )Q(λ ). We establish conditions under which nonsingular polynomial matrices A(λ ) and B(λ ) are semiscalar equivalent. As a consequence, we present the conditions of equivalence and similarity of two sets of (n× n) matrices over an arbitrary field F.