DOI link for Nondegenerate matrices
Nondegenerate matrices book
For the definitions and properties of the greatest common (left, right) divisors of the matrix polynomials, of the unimodular matrix polynomials and for their (left, right) coprimness see, for example, the books by P. J. Antsaklis and A. N. Michel [4, pp. 526-528, 535-540], C.-T. Chen [13, pp. 591-599] and T. Kailath [77, pp. 373-382].