On k-circulant matrices involving geometric sequence

In this paper we consider a k-circulant matrix with geometric sequence, where k is a nonzero complex number. The eigenvalues, the determinant, the Euclidean norm and bounds for the spectral norm of such matrix are investigated. The method for obtaining the inverse of a nonsingular k-circulant matrix, was presented in [On k-circulant matrices (with geometric sequence), Quaest. Math. 2016]. A generalization of that method is given in this paper, and using it, the inverse of a nonsingular k-circulant matrix with geometric sequence is obtained. The Moore-Penrose inverse of a singular k-circulant matrix with geometric sequence is determined in a different way than the way using in [On k-circulant matrices (with geometric sequence), Quaest. Math. 2016]