In this paper, we investigate the irreducibility of the n×n complex matrix and obtain the following result: For each A in Mn(C), let λ1, λ2,…,λm be all eigenvalues of A, where m≤n and λi≠λj if i≠j. Then A is irreducible if and only if for each P in A' (A) and P* = P = P2,we have σ(P\ker(A - λ1)) =σ(P\ker(A - λ2)) = …= σ(P\ker(A - λm)) = singleton.
