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Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra
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by
Zhaolin Jiang,
Tingting Xu,
Fuliang Lu
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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>n</mml:mi><mml:mo>×</mml:mo><mml:mi>n</mml:mi></mml:math>complex skew-circulant matrices are displayed in this paper.
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