# Math Help - Orthonormalizing a set of functions (what??)

1. ## Orthonormalizing a set of functions (what??)

Hi,

One particular question in my assignment goes like this:
"Use the Gram-Schmidt procedure in order to orthonormalize {2x, x^2, sin(x)}"

What confuses me is the fact that the question asks me to perform the Gram-Schmidt procedure on something that's not a set of vectors.

Is it even possible to project or normalize functions?

Can somebody explain this?

Thanks,
- dadads -

2. Originally Posted by dadads
Hi,

One particular question in my assignment goes like this:
"Use the Gram-Schmidt procedure in order to orthonormalize {2x, x^2, sin(x)}"

What confuses me is the fact that the question asks me to perform the Gram-Schmidt procedure on something that's not a set of vectors.

Is it even possible to project or normalize functions?

Can somebody explain this?

Thanks,
- dadads -
You need an inner product space for the Gram-Schmidt process, so we might consider the space of continuous functions on $[0,1]$ with innerproduct defined by:

$\langle f,g \rangle=\int_0^1 f(x)g(x) \; dx$

Now you can apply the G-S process.

(I am pretty sure that your assignment indicates the inner product you are supposed to use)

RonL