ON THE NORMS OF R-CIRCULANT MATRICES INVOLVING BALANCING AND LUCAS-BALANCING NUMBERS

ON THE NORMS OF R-CIRCULANT MATRICES INVOLVING BALANCING AND LUCAS-BALANCING NUMBERS

K. Prasad, M. Kumari, H. Mahato

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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.

Keywords

Balancing Number, Circulant Matrix, Determinant, Eigenvalues, Euclidean Norms, Spectral Norm.