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A New Aspect of Comrade Matrices by Reachability Matrices

  • Solary, Maryam Shams (Department of Mathematics, Payame Noor University)
  • Received : 2018.02.22
  • Accepted : 2019.01.26
  • Published : 2019.09.23

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.

Keywords

Orthogonal polynomials;companion matrix, comrade matrix, reachability matrix

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