设 a 为T的特征值,设x为对于的非零特征向量.则：Tx = ax
T^2 = T ==> T^2 x = Tx
T(T(x))=Tx
T(ax)=ax
aTx=ax
a(ax)=ax
a^2 x - ax =0
(a^2-a) x = 0
因为 x 非零向量,所以必有 a^2 - a = 0,a(a-1) = 0 ==> a = 0 或 1.