To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications

For a $q$-parameter ($q\ge2$) polynomial matrix of full rank whose regular and singular spectra have no points in common, a method for computing its partial relative factorization into a product of two matrices with disjoint spectra is suggested. One of the factors is regular and is represented as a product of $q$ matrices with disjoint spectra. The spectrum of each of the factors is independent of one of the parameters and forms in the space $\mathbb C^q$ a cylindrical manifold w.r.t. this parameter. The method is applied to computing zeros of the minimal polynomial with the corresponding eigenvectors. An application of the method to computing a basis of the null-space of polynomial solutions of the matrix that contains no zeros of its minimal polynomial is considered.