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Well, I know right that I could find a counterexample to prove that this is false. Anyone knows one? Note that $dim(V),\hspace{3.25pt}dim(W)<\infty$

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marked as duplicate by Leucippus, K B Dave, Lee David Chung Lin, Somos, dantopa Apr 8 at 3:12

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  • $\begingroup$ It's not trivial. See, e.g., this question for the standard sort of counterexample. $\endgroup$ – lulu Apr 8 at 0:42
  • $\begingroup$ Even in the case $V=W=\mathbb R$ (as vector spaces over $\mathbb R$) $T$ need not be linear. $\endgroup$ – Kavi Rama Murthy Apr 8 at 0:44
  • $\begingroup$ I'd edit the question $\endgroup$ – Esteban Vera Valdez Apr 8 at 0:58