数学：矩阵的秩的变化规律

(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)

(8)P、Q为可逆矩阵，则r(PAQ)=r(A)

(9)n阶方阵A，若|A|=0，则r(A)<n，否则r(A)=n

(10)若Ax=B有解，则r(A)=r(A,B)

(11)若A~B，则人r(A)=r(B)

(12)若所有n阶子式为零，则r(A)<t(t为A的逆序数)

(13)A中若有S阶非零子式，则r(A)>=S