In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are ...

1. INTRODUCTION. There is something fascinating about procedures for solving low degree polynomial equations. On one hand, we all know that while general solutions (using radicals) are impossible beyond the fourth degree, they have been found for quadratics, cubics, and quartics. On the other hand, the standard solutions for the the cubic and quartic are complicated, and the methods seem ad hoc...

This paper presents an overview of diierent methods proposed in the last several decades for computing the inverse of a polynomial matrix, concentrating on Buss lowicz's algorithm. A detailed description of Buss lowicz's algorithm and its sequential implementation is followed by the presentation of a new parallel algorithm, based on Buss lowicz's. The distributed and shared memory versions of t...

The eigenvalues of a matrix polynomial can be determined classically by solving a generalized eigenproblem for a linearized matrix pencil, for instance by writing the matrix polynomial in companion form. We introduce a general scaling technique, based on tropical algebra, which applies in particular to this companion form. This scaling, which is inspired by an earlier work of Akian, Bapat, and ...

This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices.

which are square invertible and have zeros – i.e. roots of detP (λ) – inside a given region Γ. We say that P (λ) is Γ-stable and call Γ the stability region. The complex stability radius rC of such polynomial matrices is the norm of the smallest perturbation ∆P (λ) . = ∆P0 +∆P1λ+ · · ·∆Pkλ k needed to “destabilize” P (λ) + ∆P (λ) and hence causing at least one zero of P (λ) + ∆P (λ) to leave th...

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...

In this paper, the problem of computing inverses of polynomial matrices has been revisited and algorithms of easy implementation are proposed to deal with either column or non-column reduced matrices. Other contributions of the paper are algorithms to perform column reduction and determinant of polynomial matrices. © 2002 Elsevier Science Inc. All rights reserved.

Amitsur's formula, which expresses det(A + B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As an applications, in up-coming papers we determine generators for the SO(n)-invariants of several matrices and relations for the O(n)-invariants of several matrices over a field of arbitrary cha...