Pour une matrice polynomiale P(x) de degr e d dans Mn;n(Kx]), o u K est un corps commutatif, une r eduction a la forme normale d'Hermite peut ^ etre calcul ee en O ~ (M(nd)) op erations arithm etiques, si M(n) est le co^ ut du produit de deux matrices n n sur K. De plus, une telle r eduction peut ^ etre obtenue en temps parall ele O(log +1 (nd)) en utilisant O(L(nd)) processeurs, si le probl em...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...

For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...