On the norms of r-circulant matrices involving balancing and Lucas-balancing numbers

Abstract

In this article, we investigate the r-circulant matrices B[r] and C[r] involving the balancing and Lucas-balancing numbers respectively with arithmetic indices. For matrices B[r] and C[r], we establish the direct formula for the eigenvalues, the determinant, the Euclidean norm and the bound for the spectral norm. Furthermore, we extend the concept to right circulant matrices and skew-right circulant matrices and, investigate all the above results including the sum identities and divisibility.