You are Here: Home >< Maths

# Euclidean vector space help watch

1. i have to orthonomalise a basis for a euclidean vector space using the Gram-Schmidt process.

The vector space is (V,w). V is the space of real polynomials of degree at most 4. I am using the standard basis for this space to begin with.
I have a function for w... w(f(X),g(X))=integral between -1 and 1 of f(X)g(X)dX.
Now I know how to run Gram-Schmidt on a normal vector space but I'm a bit confused here, my confusion stems from this function w. what am i supposed to do with it and how does it affect my orthonormal basis.
i dont want a full solution but tips and hints mainly geared towards w and its role in the vector space and the use of its function in this question would be very much appreciated!
thanks
2. w is your inner product.

An orthonormal basis is defined in terms of the inner product on the space.
3. so w is just my dot product?
4. Yes, w is your dot product/inner product/scalar product.

So it defines what it means for two basis elements to be orthogonal in your space i.e. if w(f(X),g(X))=0
5. ok thanks, thats what i originally thought but the wording of the question confused me for ages!

how would i actually normalise a polynomial? divide by w(f(x),f(x))?
6. So for example, f(X) = X and g(X) = X^2 + 1 aren't orthogonal as
7. (Original post by aqfrenzy)
ok thanks, thats what i originally thought but the wording of the question confused me for ages!

how would i actually normalise a polynomial? divide by w(f(x),f(x))?
(Assuming you are using the norm induced by the inner product which is more than likely the case) - divide by the square root of w(f(X),f(X))
8. You really shouldn't be posting questions which are for credit...
9. i was mainly asking for help with notation here...didnt understand the (V,w) bit

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 14, 2008
Today on TSR

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams