Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra

Abstract

The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra of $n\times n$ complex skew-circulant matrices are displayed in this paper.