Question

I need a pic for : If x, y in Real/ complex inner product space, and if ||x||=||y||, then x-y and x + y are orthogonal?
someone helps me, please

Answer 1

So you're supposed to demonstrate this using a picture?

Answer 2

Or you're supposed to prove it's true, so you want a picture to help you visualize it?

Answer 3

I have to have both, but I think I can handle it on algebraic way ( not 100% sure), I need see it

Answer 4

Well, I mean, there's not much to the picture really.


So the assertion is that this angle between x+y and x-y
is a right angle I'm not sure how you'd show that from this picture, I think algebraically is probably the way to prove it.