The spectral decomposition is given. Secondly, the singular g-circulant matrices are similar to the direct sum of some diagnal matrices and some nilpotency of Jordan blocks when (n,g)=1. Further, the nilpotency index of Jordan block is defined.

• 其次 ,当 (n ,g) =1时 ,给出了n级奇异g 循环矩阵相似于某些对角阵和某些幂零Jordan块的直和 ,进一步给出了其中幂零Jordan块的幂零指数的计算法