- #1
fluidistic
Gold Member
- 3,924
- 261
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.