Suppose we have a linear map $S:V \to V$ with the property that $\langle Sv,v\rangle =0$ for all $v \in V$. Then is it true that $\langle Su,v \rangle =\langle Sv,u\rangle$ for any $u,v \in V$?
2026-04-26 01:05:41.1777165541
A basic question on linear maps in inner product space
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What do you get if you expand out $ \langle S(u+v),(u+v) \rangle $?