On determinants, inverses, norms, and spread of skew circulant matrices involving the product of Pell and Pell-Lucas numbers

Abstract

In this paper, we discuss skew circulant matrices involving the product of Pell and Pell-Lucas numbers. The invertibility of the skew circulant matrices is investigated, while the fundamental theorems on the determinants and inverses of such matrices are derived by simple construction matrices. Specifically, the determinant and inverse of n × n skew circulant matrices can be expressed by the ( n − 1 ) th, n th, ( n + 1 ) th, ( n + 2 ) th product of Pell and Pell-Lucas numbers. Some norms and bounds for spread of these matrices are given, respectively. In addition, we generalized these results to skew left circulant matrix involving the product of Pell and Pell-Lucas numbers. Finally, several numerical examples are illustrated to show the effectiveness of our theoretical results.