On the determinants and inverses of R-circulant matrices with the biperiodic Fibonacci and Lucas numbers

Abstract

In this paper, we present a new generalization to compute determinants and inverses of r-circulant matrices Qn = circr ((b/a)?(2)/2 q1,(b/a)?(3)/2 q2,..., (b/a)?(n+1)/2 qn) and Ln = circr ((b/a)?(1)/2 l1,(b/a)?(2)/2 l2,..., (b/a)?(n)/2 ln) whose entries are the biperiodic Fibonacci and the biperiodic Lucas numbers, respectively. Also, we express determinants of the matrices Qn and Ln by using only the biperiodic Fibonacci and the biperiodic Lucas numbers.