WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Efficient Algorithms for Finding the Minimal Polynomials and the Inverses of Level-k FLS (r1, ..., rk)-Circulant Matrices
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Abstract: The level-k FLS (r1, . . . , rk)-circulant matrix over any field is introduced. The diagonalization and spectral decomposition of level-k FLS (r1, . . . , rk)-circulant matrices over any field are discussed. Algorithms for computing the minimal polynomial of this kind of matrices over any field are presented by means of the algorithm for the Gr¨obner basis of the ideal in the polynomial ring, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with level-k FLS (r1, . . . , rk)-circulant blocks over any field is given by using the Schur complement, which can be realized by CoCoA 4.0, an algebraic system, over the field of rational numbers or the field of residue classes of modulo prime number.
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Keywords: Level-k FLS (r1, . . . , rk)-circulant matrix, minimal polynomial, inverse, diagonalization, spectral decomposition, Grobner basis