- #1

fluidistic

Gold Member

- 3,741

- 124

## Homework Statement

I'm trying to follow the demonstration of the Cauchy-Schwarz's inequality proof given in http://mathworld.wolfram.com/SchwarzsInequality.html.

I am stuck at the last step, namely that [itex]\langle \bar g , f \rangle \langle f , \bar g \rangle \leq \langle \bar f , f \rangle \langle \bar g , g \rangle \Rightarrow |\langle f , g \rangle |^2 \leq \langle f , f \rangle \langle g , g \rangle[/itex].

## Homework Equations

I don't know.

## The Attempt at a Solution

[itex]\langle \bar g , f \rangle \langle f , \bar g \rangle \leq \langle \bar f , f \rangle \langle \bar g , g \rangle \Rightarrow \langle \bar f , g \rangle \langle \bar f , g \rangle \leq \langle \bar f , f \rangle \langle \bar g , g \rangle[/itex]. I'm stuck here.

I know that [itex]||f||=\sqrt {\langle f , f \rangle}[/itex] but I don't even know if I can use this fact. Any tip is appreciated.