17/11/23 01:57:57.79 A+tqw7ij.net
>>649
(1) AB = 0 → Im(B) ⊂ ker(A)
→ rank(B) = dim(Im(B)) ≦ dim(ker(A)) = n － dim(Im(A)) = n － rank(A)
→ rank(A) + rank(B) ≦ n
(2) A+B = E → Im(A) + Im(B) = K^n
→ rank(A) + rank(B) = dim(Im(A)) + dim(Im(B)) ≧ n
17/11/23 01:57:57.79 A+tqw7ij.net
>>649
(1) AB = 0 → Im(B) ⊂ ker(A)
→ rank(B) = dim(Im(B)) ≦ dim(ker(A)) = n － dim(Im(A)) = n － rank(A)
→ rank(A) + rank(B) ≦ n
(2) A+B = E → Im(A) + Im(B) = K^n
→ rank(A) + rank(B) = dim(Im(A)) + dim(Im(B)) ≧ n