### EFFICIENT ALGORITHMS FOR COMPUTING THE MINIMAL POLYNOMIALS AND THE INVERSES OF LEVEL-k Π-CIRCULANT MATRICES

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Jiang, Zhaolin;Liu, Sanyang

• 발행 : 2003.08.01
• 30 4

#### 초록

In this paper, a new kind of matrices, i.e., $level-{\kappa}$ II-circulant matrices is considered. Algorithms for computing minimal polynomial of this kind of matrices are presented by means of the algorithm for the Grobner 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.

#### 키워드

Grobner basis;minimal polynomial;level-k II-circulant matrix;inverse

#### 참고문헌

1. J. Algebra v.100 pp.138-178 New constructive methods in classical ideal theory H.M.Moller;F.Mora https://doi.org/10.1016/0021-8693(86)90071-2
2. Circulant Matrices J.Zhaolin;Z.Zhangxin
3. Kyung-pook Math. J. v.25 pp.71-75 The structure of multiblock circulants J.Baker;F.Hiergeist;G.Trapp
4. Algorithmic Algebra B.Mishra
5. J. Combin. Theory, Series A v.40 pp.125-135 Construction of D-optimal designs for N=2 mod 4 using block-circulant matrices TH.Chadjipantelis;STR.Kounias;CHR.Moyssiadis https://doi.org/10.1016/0097-3165(85)90051-2
6. J. London Math. Soc. v.8 pp.190-196 Injective envelopes and inverse polynomials D.G.Northcott
7. Amer. Math. Monthly. v.62 pp.303-308 Methods of matrix inversion D.Greenspan https://doi.org/10.2307/2307034
8. Amer. Math. Soc. An introduction to Grobner bases W.W.Adams;P.Loustaunau

#### 피인용 문헌

1. 1. Inversion of two new circulant matrices over Zm vol.81, 2017, doi:10.4134/BKMS.2003.40.3.425