Let $X$ be (possibly infinite-dimensional) Hilbert space. How can we show that if $$\langle a,x\rangle = \langle b,x\rangle,\forall x\in X$$ then $a=b$?
2026-04-04 08:41:22.1775292082
Why $\langle a,x\rangle = \langle b,x\rangle,\forall x\in X\implies a=b$
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Hint. Let $x = a-b$, and use $\langle y,y\rangle = 0 \iff y = 0$.