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Bull. Korean Math. Soc. 2003; 40(3): 425-435

Printed September 1, 2003

Copyright © The Korean Mathematical Society.

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

Zhaolin Jiang and Sanyang Liu

Xidian University, Xidian University

Abstract

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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

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