- #1
Mr Davis 97
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Homework Statement
Let ##V## be a vector space equipped with an inner product ##\langle \cdot, \cdot \rangle##. If ##\langle x,y \rangle = \langle x, z\rangle## for all ##x \in V##, then ##y=z##.
Homework Equations
The Attempt at a Solution
Here is my attempt. ##\langle x,y \rangle = \langle x, z\rangle## means that ##\langle x,y \rangle - \langle x, z\rangle = 0##, and so ##\langle x, y - z\rangle = 0##. This is as far as I've gotten. I don't see how to deduce that ##y - z = 0##.