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Linear Algebra Help!!

Let Ω = [−1, 1] ⊂ R and consider Π2(Ω) and given that B = {p1, p2, p3} is a basis of Π2(Ω) and that <f | g> = f(−1)g(−1) + f(0)g(0) + f(1)g(1)
does defines an inner product on Π2(Ω), consider the following:

Show that B is not an orthonormal basis of (Π2(Ω),<.,.>).

I'm not very confident with orthonormal basis' so any help to try and make me answer this question will be much appreciated.
How far does your limited knowledge extend huh Zack?
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Original post by Pablo Picasso
How far does your limited knowledge extend huh Zack?


Zack??
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Original post by AFraggers


I'm not very confident with orthonormal basis' so any help to try and make me answer this question will be much appreciated.


What does it mean for B to be an orthogonal basis of (...)? What about that is patently untrue or that you can show is untrue?
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Original post by Zacken
What does it mean for B to be an orthogonal basis of (...)? What about that is patently untrue or that you can show is untrue?


I'm not sure. I've only come across questions similar to this when B is given. I don't really know where to start without B.
Well for a basis to not be orthonormal what do you need?

A basis is orthonormal if the inner product of an element in the basis with itself is 1, and the inner product of any two distinct elements is 0.

So find two distinct elements in the basis which when you perform the inner product on, does not give you zero, or find an element such that the inner product with itself is not equal to 1.
And I'm not quite sure what we have a basis for. What is Π2(Ω)?
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Original post by Phoebe Buffay
And I'm not quite sure what we have a basis for. What is Π2(Ω)?


There is more parts to this question hence the basis. Also Π2 means the space of all real functions with domain Ω
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Original post by Phoebe Buffay
Well for a basis to not be orthonormal what do you need?

A basis is orthonormal if the inner product of an element in the basis with itself is 1, and the inner product of any two distinct elements is 0.

So find two distinct elements in the basis which when you perform the inner product on, does not give you zero, or find an element such that the inner product with itself is not equal to 1.


Can you give me a starting block as to where I can find these 2 distinct elements

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