I need to prove that:
norm ||x||=||y|| implies that inproduct < x+y,x-y > = 0
I thought about it for a long time, but I don't come any further.
I've got that:
< x+y,x-y > = <x,x> + <x,y> - <y,x> - <y,y>
= ||x||^2 + <x,y> - <y,x> - ||y||^2
So somehow ||x||=||y|| implies that <x,y> = <y,x>
I thought of using Cauchy-Schwartz, the triangle inequality or the parallelogram law..
Can someone finish the prove?