On k-circulant matrices involving the Fibonacci numbers

Let k be a nonzero complex number. In this paper we consider a k-circulant matrix whose first row is (F1,F2,...,Fn), where Fn is the n^{th} Fibonacci number, and investigate the eigenvalues and Euclidean (or Frobenius) norm of that matrix. Also, the upper and lower bounds for the spectral norm of the Hadamard inverse of that matrix are obtained.