Reduction of matrices by means of equivalent transformations and similarity transformations

The structure of polynomial matrices in connection with their reducibility by semiscalar-equivalent transformations and similarity transformations to simpler forms is considered. In particular, the canonical form of polynomial matrices without multiple characteristic roots with respect to the above transformations is indicated. This allows one to establish a canonical form with respect to similarity for a certain type of finite collections of numerical matrices. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 769–782, November, 1998.