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!