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

Asked Apr 21 '12 at 03:47

Active Apr 21 '12 at 09:38

Viewed 920 times

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 $L^2$.

edited Apr 21 '12 at 09:38

Davide Giraudo

asked Apr 21 '12 at 03:47

Misaj

3

$\langle \nabla f, \nabla g\rangle_{L^2(\Omega)} = \sum_i \int_\Omega \partial_i f, \partial_i g, dx$. – martini Apr 21 '12 at 04:53
@martini As I expected! Thanks a lot. – Misaj Apr 21 '12 at 04:57
1

@Ashuley Use '\langle \rangle' which gives $\langle \rangle$ instead of $<>$. – Davide Giraudo Apr 21 '12 at 09:39
@martini How about $\langle f, g \rangle \text{where} f(x,y) \text{and } g(x,y)$? Thanks – KYHSGeekCode Sep 07 '18 at 11:34

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