On the reduction of a set of numerical matrices to quasi-diagonal form with one similarity transformation

We consider finite sets of numerical matrices and the polynomial matrices corresponding to them that have the Smith form diag (1, (x), ..., (x)). We solve the problem of reducing such sets to canonical form with one similarity transformation assuming that all the roots of the invariant polynomial (x) are simple.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 101–105.