In this paper, algorithms for the computation of all matrices of the generalized polynomial Bezout identity are proposed. The algorithms are based on the computation of minimal polynomial basis for the right null spaces of certain polynomial matrices. For this reason, an algorithm for the computation of minimal polynomial bases is also proposed. Since this algorithm relies solely on singular va...

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

We introduce a method and algorithm for computing the weighted MoorePenrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [24] to multiple variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Al...

In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices. Discrete Fourier transform enables us to propose a new algorithm based on uniform sampling of polynomial matrices in frequency domain. This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decompos...