Abstract: In this paper, we give the explicit expressions of level-k circulant matrices of type (n₁,n₂,…n_k) and of order n₁n₂…n_k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.

Key words: level-k circulant matrices of type(n₁,n_?,…,n_k), explicit expressions, eigenvalues, determinants, inverse matrices unitarily diagonalizable