On k-circulant matrices involving geometricsequence

Abstract

In this paper we consider ak-circulant matrix with geometric sequence, wherekis anonzero complex number. The eigenvalues, the determinant, the Euclidean norm andbounds for the spectral norm of such matrix are investigated. The method for obtainingthe inverse of a nonsingulark-circulant matrix, was presented in [Onk-circulant matrices(with geometric sequence), Quaest. Math. 2016]. A generalization of that method is givenin this paper, and using it, the inverse of a nonsingulark-circulant matrix with geometricsequence is obtained. The Moore-Penrose inverse of a singulark-circulant matrix withgeometric sequence is determined in a different way than the way using in [Onk-circulantmatrices (with geometric sequence), Quaest. Math. 2016].