å¦Am*nç©éµï¼å¦ä¸ç©éµB:
1ãA为
满秩ç©éµæ¶ï¼år(AB)=r(BA)=r(B);
2ãA为è¡æ»¡ç§©ç©éµæ¶ï¼år(BA)=r(B);
3ãA为å满秩ç©éµæ¶ï¼år(AB)=r(B).
A为满秩ç©éµ
é£ä¹Aæ¯å¯éæ¹éµ
ä¸æ¹é¢æ r(AB) <= r(B)
å¦ä¸æ¹é¢ r(B) = r(A^-1(AB)) <= r(AB)
æ以 r(AB) = r(B).
A为å满秩ç©éµæ¶
èè
é½æ¬¡çº¿æ§æ¹ç¨ç» ABX=0 ä¸ BX = 0
å 为 A为å满秩, æ以 A(BX)=0 åå¿
æ BX=0. æ
å®ä»¬å解ã
秩ç¸çã