On <i>k</i>-circulant matrices (with geometric sequence)

Abstract

Let k be a nonzero complex number. In this paper we show how the inverse of a nonsingular k-circulant matrix can be obtained. The method is used to determine the inverse of a nonsingular k-circulant matrix with geometric sequence. If k = 1, then we get the result presented in the paper A.C.F. Bueno, Right Circulant Matrices With Geometric Progression, Int. J. Appl. Math. Res. 1(4) (2012), 593-603. Also, we derive the Moore-Penrose inverse of a singular k-circulant matrix with geometric sequence. At the end of the paper, we illustrate the obtained results by examples.

Keywords: k-circulant matrix, inverse, Moore-Penrose inverse, geometric sequence