Must $T:V \to V$ be the $0$ transformation if $\langle T(v),u\rangle=0 \ \forall u,v \in V$?
My intuition say $T$ must be the $0$ transformation, can someone give me a formal proof please?
2026-04-13 12:06:32.1776081992
Must $T:V \to V$ be the $0$ transformation if $\langle T(v),u\rangle=0 \forall u,v \in V$?
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Pick $u=T(v)$, then this implies $T(v)=0$ for all $v\in V$.