let S and T be linear transformation on n-dimensional vector space
why is dim ker(ST) less than dim ker(S) + dim ker(T)
Actually, would it be always less than? I always thought it could be less than or equals, am I right on this?
Say like if matrix A times B, then rank(AB) <= min(rank(A), rank(B)), is this right? And then apply this same idea to the nullspace too, would it all come out right?
ohh...
So am I right to say about $\displaystyle rank(AB) \leq min(rank(A), rank(B))$? That's the rank of $\displaystyle AB$ would always be less than or equals to the minimum rank between rank(A) and rank (B)?