Numerical computation of minimal polynomial bases: A generalized resultant approach

We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F(s). The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be implemented using only orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coefficients.