Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $L^2$.

share|cite|improve this question
2  
$\langle \nabla f, \nabla g\rangle_{L^2(\Omega)} = \sum_i \int_\Omega \partial_i f\, \partial_i g\, dx$. – martini Apr 21 '12 at 4:53
    
@martini As I expected! Thanks a lot. – Misaj Apr 21 '12 at 4:57
1  
@Ashuley Use '\langle \rangle' which gives $\langle \rangle$ instead of $<>$. – Davide Giraudo Apr 21 '12 at 9:39

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.