Bessel's inequality proof

Hi guys.

I need to prove Bessel's inequality for a finite set of orthonormal vectors

I looked around the internet and found this on Wikipedia:

"Bessel's inequality follows from the identity:

"

but something just does not make sense to me.

how did they make the first transition from to ?

you can't just use the binomial expanding formula here, can you?

Is there another, more simple proof for this inequality?

Thanks in advanced!

Re: Bessel's inequality proof

Quote:

Originally Posted by

**Stormey** Hi guys.

I need to prove Bessel's inequality for a finite set of orthonormal vectors

This is one I have used.

Let

Re: Bessel's inequality proof

Great. thank you.

that's more clear.

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Re: Bessel's inequality proof

Hi,

The proof that you indicate is not hard to understand. It mainly uses distribution of inner product (dot product) over addition.

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