Degrees of greatest common divisors of invariant factors of two regular polynomial matrices
Stephanie J. Barnett · Mathematical Proceedings of the Cambridge Philosophical Society · 1969
Abstract In a previous paper it was shown that a necessary and sufficient condition for two regular polynomial matrices T and U to have relatively prime determinants is that a certain matrix R be non-singular. This generalization of the resultant of two scalar polynomials is extended to give an expression for the sum of the degrees of the greatest common divisors of all pairs of invariant factors of T and U in terms of the rank of R. Further, if rank R exceeds a given value then specified pairs of factors are relatively prime.