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 Efficient algorithms for computing the minimal polynomials and the inverses of level-$k$ $\Pi$-circulant matrices Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 425-435 Published online September 1, 2003 Zhaolin Jiang and Sanyang Liu Xidian University, Xidian University Abstract : In this paper, a new kind of matrices, i.e., level-$k$ $\Pi$-circulant matrices is considered. Algorithms for computing minimal polynomial of this kind of matrices are presented by means of the algorithm for the Gr\"{o}bner basis of the ideal in the polynomial ring. Two algorithms for finding the inverses of such matrices are also presented based on the Buchberger's algorithm. Keywords : Grobner basis, minimal polynomial, level-$k$ $\Pi$-circulant matrix, inverse MSC numbers : 15A21, 65F15 Downloads: Full-text PDF