Revisiting the Matrix Polynomial Greatest Common Divisor

In this paper, we revisit the greatest common right divisor (GCRD) extraction from a set of polynomial matrices , with coefficients in generic field and column dimension . We give necessary sufficient conditions for matrix to be GCRD using Smith normal form compound obtained by concatenating vertically, where also describe complete degrees freedom solution link it Hermite then an algorithm constructing particular minimum size problem when or state-space techniques. This new method works directly on coefficient orthogonal transformations only. The is based staircase algorithm, applied pencil derived generalized model