A COMPUTATION PERSPECTIVE FOR THE EIGENVALUES OF CIRCULANT MATRICES INVOLVING GEOMETRIC PROGRESSION

Abstract

In this article, the eigenvalues and inverse of circulant matrices with entries in the first row having the form of a geometric sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant and inverse is simply using elementary row or column operations. For the eigenvalues, the known formulation of the previous results is simplified by considering the specialty of the sequence and using cyclic group properties of unit circles in the complex plane. Then, the algorithm of eigenvalues formulation is constructed, and it shows as a better computation method.

Keywords

• circulant matrix, eigenvalues
• inverse
• cyclic group
• geometric sequence