# Schwarz Inequality

Hello,

I'm having a small problem with Schwarz inequality, |u⋅v|≤||u||||v||

the statement is true if and only if cosΘ≤1 !!, I'm familiar with this result but how could it be more than 1?
what is so special in higher dimensions that it gave the ability for cosine to be more than 1? why and how?

Related Linear and Abstract Algebra News on Phys.org
Fredrik
Staff Emeritus
$$\cos\theta =\frac{\langle u,v\rangle}{\|u\|\|v\|}.$$ This isn't some new version of the cosine function. It's the plain old cosine function that you're familiar with.