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How can we define the Inner Product of multi-variable functions?

For example, what is the value of the inner product of $\nabla f$ and $\nabla g$?

$\langle \nabla f, \nabla g\rangle = ?? $

Here $\langle\cdot,\cdot\rangle$ is used for the inner product in $L^2$.

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    @martini How about $\langle f, g \rangle \text{where} f(x,y) \text{and } g(x,y)$? Thanks2018-09-07

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