On k-circulant matrices (with geometric sequence)

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.