Restating the question in the title:
Suppose $V$ is a finite dimensional vector space and $S$ and $T$ are linear maps within $V$. Then is $ dim(S(ImT)) = rank (ST)$? If not, then what is $dim(S(ImT))$?
Also, is $dim(S(ImT)) \leq rankS$?
2026-04-03 04:19:47.1775189987
Let $V$ be a finite dimensional vector space and $S,T:V \rightarrow V$ be linear. Is $ dim(S(ImT)) = rank (ST)$?
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