Open Access
2014 On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices
Zhaolin Jiang
Abstr. Appl. Anal. 2014(SI53): 1-10 (2014). DOI: 10.1155/2014/521643

Abstract

Circulant matrices have important applications in solving various differential equations. The level-k scaled factor circulant matrix over any field is introduced. Algorithms for finding the minimal polynomial of this kind of matrices over any field are presented by means of the algorithm for the Gröbner 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 computing the inverse of partitioned matrix with level-k scaled factor circulant matrix 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.

Citation

Download Citation

Zhaolin Jiang. "On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices." Abstr. Appl. Anal. 2014 (SI53) 1 - 10, 2014. https://doi.org/10.1155/2014/521643

Information

Published: 2014
First available in Project Euclid: 27 February 2015

MathSciNet: MR3219375
Digital Object Identifier: 10.1155/2014/521643

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI53 • 2014
Back to Top