(aa^T)a=a(a^Ta)=a
故1为aa^T的特征值
又r(aa^T)=1故0为其2重特征值.
故E-aaT的特征值为0,1,1
故E-aaT的秩为2.
扩展资料
矩阵的秩变化规律
(1)转置后秩不变
(2)r(A)<=min(m,n),A是m*n型矩阵
(3)r(kA)=r(A),k不等于0
(4)r(A)=0 <=> A=0
(5)r(A+B)<=r(A)+r(B)
(6)r(AB)<=min(r(A),r(B))
(7)r(A)+r(B)-n<=r(AB)
参考资料
(aa^T)a=a(a^Ta)=a
故1为aa^T的特征值
又r(aa^T)=1故0为其2重特征值.
故E-aaT的特征值为0,1,1
故E-aaT的秩为2.
矩阵的秩变化规律
(1)转置后秩不变
(2)r(A)<=min(m,n),A是m*n型矩阵
(3)r(kA)=r(A),k不等于0
(4)r(A)=0 <=> A=0
(5)r(A+B)<=r(A)+r(B)
(6)r(AB)<=min(r(A),r(B))
(7)r(A)+r(B)-n<=r(AB)
参考资料
