In this paper a new construction of MDS array codes is introduced. In order to obtain a code with this property, the parity-check matrix is constructed just using a superregular matrix by blocks composed by powers of the companion matrix of a primitive polynomial. Also a decoding algorithm for these codes is introduced.

In this paper we find new estimate for the numerical radius of a given matrix, and we prove that, this estimate is better than any estimate for the numerical radius. We present also new bounds for the zero of polynomials by using new estimate for the numerical radius of a companion matrix of a given polynomial and matrix inequalities.

Older adults with strong social connections are at a reduced risk for health problems and mortality. We describe two field studies to inform the development of a virtual agent designed to provide long-term, continuous social support to isolated older adults. Findings include the topics that older adults would like to discuss with a companion agent, in addition to overall reactions to interactin...

8 Matrices 16 8.1 Representation of vector spaces and linear transformations . . . . . . . . . . . . . . . 16 8.2 Similarity transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 8.3 Direct sums of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 8.4 The companion matrix of a polynomial . . . . . . . . . . . . . . . . . . . . . . . ....

Abstract This study is devoted to some periodic matrix difference equations, through their associated product of companion matrices in blocks. Linear recursive sequences the algebra square blocks and generalized Cayley–Hamilton theorem are considered for working out results about powers Two algorithms computing finite built. Illustrative examples applications demonstrate effectiveness our appro...

The aim of this paper is to construct cyclic subgroups the projective general linear group over from companion matrix, and then form caps various degrees in . Geometric properties these as secant distributions index are given determined if they complete. Also, partitioned into disjoint lines discussed.

Univariate polynoimial rootnding is an oldest classical problem, which is still an important research topic, due to its impact on computational algebra and geometry. The Weierstrass (Durand{Kerner) approach and its variations are most popular practical choices for simultaneous approximation of all roots of a polynomial, but these methods require computations with a high multiple precision. We a...

We employ several numerical radius inequalities to the square of Frobenius companion matrices monic matrix polynomials provide new bounds for eigenvalues these polynomials.