Bezout equations over bivariate polynomial matrices related by an entire function

This study addresses Bezout equations over bivariate polynomial matrices, where the relationship between two variables is described by a real entire function. This paper proposes a solution method that makes optimal use of minor primeness to reduce such Bezout equations to simple equations over univariate scalar polynomials. The proposed solution method requires only matrix calculations, thus making it very useful, especially in the absence of modern computer algebra systems.