L^2 Scalar Product for Complex-Valued Functions

[ConeOfIce]

Homework Statement

Consider the vector space of square integrable complex-valued functions
in one dimension V = L^2(R) = {f(x) : interal|f(x)|^2dx < ∞}. Show that
<f|g> = integral f(x)*g(x)dx defines a scalar product on this vector space.

The Attempt at a Solution

I actually have no clue where I even start with this question. I have not learned the Laplace function before, though I have a basic idea of how it works. Any help on how I might go at this question would be very appreciated.

 

[genneth]

I don't see what this has to do with a "Laplace function" whatever that is. This is an elementary question about vector spaces and scalar products. You've been given the space, and the inner product, so you just have to verify that it does indeed work like a scalar product.

So: what are the properties that define a scalar product?

 

[ConeOfIce]

Sorry, the L was supposed to be the symbol for the Laplace function, does it still not make a difference?

 

[genneth]

The L does not represent a function. It's notation for the set of L^2 integrable functions over R, as defined right afterwards.