On the Norms of some Special Matrices with Padovan and Pell-Padovan-Like Sequence

Abstract

The focus of this paper is to define some special matrices like r−circulant, circulant, semi-circulant, Hankel and Toeplitz matrices with the help of integer sequences. In particular, this work is focusing on obtaining norms of the aforementioned types of matrices that are involved with Pell-Padovan-like sequences. Furthermore, the upper and lower bounds of spectral norms of those matrices have
been also determined.

Key words and phrases. Padovan sequence, Pell-Padovan-like sequence, circulant, r−circulant, spectral norm, Euclidean norm.

2000 Mathematics Subject Classification. 15A45, 15A60, 15A36, 11B39