Efficient algorithms for computing the minimal polynomials and the inverses of level-$k$ $\Pi$-circulant matrices

Abstract

In this paper, a new kind of matrices, i.e., level-kPi-circulant matrices is considered. Algorithms for computingminimal polynomial of this kind of matrices are presented by meansof the algorithm for the Gr"{o}bner basis of the ideal in thepolynomial ring. Two algorithms for finding the inverses of suchmatrices are also presented based on the Buchberger's algorithm.