Exploring Orthogonality in Linear Algebra: A Simple Proof of a Common Identity

[EvLer]

In one of my homework problems we are asked to prove this:

|X + Y|^2 + |X - Y|^2 = 2|X|^2 + 2|Y|^2

It seems quite simple: I just expanded both of them (cancelled 2(X dot Y) terms) and came up with the expression on the right. Is there something I am missing or is it really that simple?

Thanks !

 

[Hurkyl]

It really is!

 

[mathwonk]

linear algebra makes many questions in geometry rather trivial. for this reason high schools should teach the subject, instead of calculus, where they usually do an extremely bad job.