Canonical form with respect to semiscalar equivalence for a matrix pencil with nonsingular first matrix - Prokip, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
Polynomial matrices A(x) and B(x) of size n × n over a field F are called semiscalar equivalent if there exist a nonsingular n × n matrix P over F and an invertible n × n matrix Q(x) over F[x] such that A(x) = PB(x)Q(x). We give a canonical form with respect to the semiscalar equivalence for a matrix pencil A(x) = A_0x - A_1, where A_0 and A_1 are n × n matrices over F, and A_0 is nonsingular.