On common monic divisors having a given canonical diagonal form for matrix polynomials

Under certain restrictions we give a condition for the existence of common monic divisors having a given diagonal form for nonsingular matrix polynomials, and we propose a method of finding them. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 28–32.