We show that the computation of the Popov form of Ore polynomial matrices can be formulated as a problem of computing the left nullspace of such matrices. While this technique is already known for polynomial matrices, the extension to Ore polynomial matrices is not immediate because multiplication of the matrix entries is not commutative. A number of results for polynomial matrices are extended...

Computing roots of scalar polynomials as the eigenvalues of Frobenius companion matrices using backward stable eigenvalue algorithms is a classical approach. The introduction of new families of companion matrices allows for the use of other matrices in the root-finding problem. In this paper, we analyze the backward stability of polynomial root-finding algorithms via Fiedler companion matrices....

The main purpose of this work is to propose new notions of equivalence between polynomial matrices, that preserve both the finite and infinite elementary divisor structure. The approach we use is twofold : a) the ”homogeneous polynomial matrix approach” where in place of the polynomial matrices, we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order ...