The double Capelli polynomial of total degree 2t is

If a system is given by its transfer function then the stability of the system is determined hy the denominator polynomial and its corresponding Hurwitz matrix 7-{. Also the critical stability conditions are determined by its determinant det 7-{. The aim of this paper is to get a generalized Hurwitz matrix for polynomial matrices. In order to achieve that, we first obtain a relation between the...

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 imple...

let $d$ be a digraph with skew-adjacency matrix $s(d)$‎. ‎the skew‎ ‎energy of $d$ is defined as the sum of the norms of all‎ ‎eigenvalues of $s(d)$‎. ‎two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎we establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energ...

In this paper we discuss the problem of computing the real radius of controllability of the Single Input Multi Output (SIMO) systems described by univariate polynomial matrices. The problem is equivalent to computing the nearest noncoprime polynomial matrix to the polynomial matrix describing the system in some prescribed norm. A particular case of this problem is to compute approximate GCD of ...

In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen a...

An algorithm is described for extracting a polynomial matrix factor featuring any subset of the zeros of a given non-singular polynomial matrix. It is assumed that the zeros to be extracted are given as input data. Complex or repeated zeros are allowed. The algorithm is based on interpolation and relies upon numerically reliable subroutines only. It makes use of a procedure that computes the ge...

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

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 ...

For a nonnegative n× n matrix A, we find that there is a polynomial f(x) ∈ R[x] such that f(A) is a positive matrix of rank one if and only if A is irreducible. Furthermore, we show that the lowest degree such polynomial f(x) with tr f(A) = n is unique. Thus, generalizing the well-known definition of the Hoffman polynomial of a strongly connected regular digraph, for any irreducible nonnegative...