On Q-circulant matrices

In this paper, we generalize the concepts of circulant matrix, r-circulant matrix, \((r,\,m)\) $(r,m)$ -circulant like matrix, H-circulant matrix and s-H-circulant matrix, and a new type of matrix called Q-circulant matrix is introduced, where Q is a non-derogatory matrix. The algebraic structure, eigenvalues and inverses of Q-circulant matrices are studied. Moreover, the eigenvalues of Q-circulant matrices whose entries are Horadam, Fibonacci, Jacobsthal, Pell numbers and arithmetic sequences are given.