A standard way of dealing with a matrix polynomial P(λ) is to convert it into an equivalent
matrix pencil—a process known as linearization. For any regular matrix polynomial, a new …

Linearizations of singular matrix polynomials and the recovery of minimal indices Page 1 ELA
LINEARIZATIONS OF SINGULAR MATRIX POLYNOMIALS AND THE RECOVERY OF MINIMAL …

In this paper, we obtain formulas for the left and right eigenvectors and minimal bases of
some families of Fiedler-like linearizations of square matrix polynomials. In particular, for the …

We present a new algorithm for computing a μ-basis of the syzygy module of n polynomials
in one variable over an arbitrary field K. The algorithm is conceptually different from the …

We discuss computationally efficient and numerically reliable algorithms to compute minimal
proper nullspace bases of a rational or polynomial matrix. The underlying main …

We develop a theory and an algorithm for constructing minimal-degree polynomial moving
frames for polynomial curves in an affine space. The algorithm is equivariant under volume …

We revisit the notion of root polynomials, thoroughly studied in (Dopico and Noferini, 2020
[9]) for general polynomial matrices, and show how they can efficiently be computed in the …

The standard way of solving a polynomial eigenvalue problem associated with a matrix
polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil …

In this paper, we present an improved algorithm to compute the minimal null-space basis of
polynomial matrices, a problem which has many applications in control and systems theory …

Polynomial minimal bases of rational vector subspaces are a classical concept that plays an
important role in control theory, linear systems theory, and coding theory. It is a common …