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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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KYUNGPOOK Math. J. 2019; 59(3): 505-513

Published online September 23, 2019

Copyright © Kyungpook Mathematical Journal.

A New Aspect of Comrade Matrices by Reachability Matrices

Department of Mathematics, Payame Noor University, P. O. Box 19395-3697 Tehran, Iran
e-mail : shamssolary@pnu.ac.ir, shamssolary@gmail.com

Received: February 22, 2018; Revised: January 22, 2019; Accepted: January 26, 2019

Abstract

In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.