let $cr_n(f_p)$ denote the algebra of $n times n$ circulant‎ ‎matrices over $f_p$‎, ‎the finite field of order $p$ a prime‎. ‎the‎ ‎order of the unit groups $mathcal{u}(cr_3(f_p))$‎, ‎$mathcal{u}(cr_4(f_p))$ and $mathcal{u}(cr_5(f_p))$ of algebras of‎ ‎circulant matrices over $f_p$ are computed‎.

We solve Olga Taussky–Todd’s circulant problem in the case of order 16.

In the present paper, we give upper and lower bounds for the spectral norm of g-circulant matrix, whose the rst row entries are the classical Horadam numbers U (a,b) i . In addition, we also establish an explicit formula of the spectral norm for g-circulant matrix with the rst row ([U (a,b) 0 ] , [U (a,b) 1 ] , · · · , [U (a,b) n−1 ]).

A circulant (di)graph is a (di)graph on n vertices that admits a cyclic automorphism of order n. This paper provides a survey of the work that has been done on finding the automorphism groups of circulant (di)graphs, including the generalisation in which the edges of the (di)graph have been assigned colours that are invariant under the aforementioned cyclic automorphism. Mathematics Subject Cla...

In this work we present some matrix operators named circulant operators and their action on square matrices. This study on square matrices provides new insights into the structure of the space of square matrices. Moreover it can be useful in various fields as in agents networking on Grid or large-scale distributed self-organizing grid systems. Keywords— Pascal matrices, Binomial Recursion, Circ...

In this paper, we study norms of circulant matrices H = Circ(H 0 , H (k) 1 , . . . ,H (k) n−1) , H = Circ(H k , H (1) k , . . . ,H (n−1) k ) and r−circulant matrices Hr = Circr(H 0 ,H 1 , . . . ,H n−1) , Hr = Circr(H (0) k ,H (1) k , . . . ,H (n−1) k ) , where H (k) n denotes the n th hyperharmonic number of order r. Mathematics subject classification (2010): 15A60, 15B05, 11B99.

We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here “binary matrix” means a matrix whose elements are drawn from {0, 1} or {−1, 1}. We describe efficient parallel algorithms for the search, using Duval’s algorithm for generation of Lyndon words and the well-known representation of the determinant of a circulant in terms of roots of unity....

In this paper a method is proposed called circulant matching method to approximate the superposition of a number of discrete time batch Markovian arrival sources by a circulant batch Markovian process while matching the stationary cumulative distribution and the autocorrelation sequence of the input rate process Special attention is paid to periodic sources The method is applied to the superpos...

Boundary value methods (BVMs) for ordinary di erential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditio...

Owing to its orthogonality, simplicity of the inversion and fast algorithms, Jacket transform generalising from the Hadamard transform has played important roles in signal and image processing, mobile communication for coding design, cryptography, etc. In this paper, inspired by the emerging block Jacket transform, a new class of circulant block Jacket matrices (CBJMs) are mathematically define...