Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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

I'm currently trying to solve an equation of the form $$f(x) = \sum_m\,a_m\,\varphi_m(x)$$ and it's required me to project this equation on a different set of functions $$\{\phi_m(x)\}$$ that is orthonormal on the interval (a,b).

How do I execute such kind of projection?

share|cite|improve this question
The question is not clear. Your $f$ is already a linear combination of $\{\varphi_m\}$. Can you make your question more clear? – Siminore Sep 1 '12 at 9:58
Sorry, I wrote it wrong... the basis is different from the other one :) – Juan Sebastian Totero Sep 1 '12 at 10:42
up vote 1 down vote accepted

I think the coefficients of $f$ on the new basis should be given by

\begin{align} a'_n=\int_a^b f(x)\phi_n(x)w(x)dx &=\int_a^b \sum_m a_m\varphi_m(x)\phi_n(x)w(x)dx\\ &=\sum_m a_m\int_a^b \varphi_m(x)\phi_n(x)w(x)dx\\ \end{align}

supposing the integral-sum exchange is possible and where $w(x)$ is the weight function of the given scalar product.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.