On k-Circulant Matrices with Arithmetic Sequence

Abstract

Let k be a nonzero complex number. In this paper we consider k-circulant matrices with arithmetic sequence and investigate the eigenvalues, determinants and Euclidean norms of such matrices. Also, for k=1, the inverses of such (invertible) matrices are obtained (in a way different from the way presented in the paper: M. Bahsi and S. Solak, On the Circulant Matrices with Arithmetic Sequence, Int. J. Contemp. Math. Sci. 5(25) (2010), 1213-1222, and the Moore-Penrose inverses of such (singular) matrices are derived.