The inverse and the Moore-Penrose inverse of a $k$-circulant matrix with binomial coefficients

Abstract

Let $k$ be a non-zero complex number. In this paper, we consider a $k$-circulant matrix with binomial coefficients. The inverse of such invertible matrix is determined. We also obtain the Moore\,-\,Penrose inverse (and the group inverse) of such singular matrix. The obtained results are illustrated by examples at the end of this paper.