(adsbygoogle = window.adsbygoogle || []).push({}); Help with Cauchy-Schwarz Inequality proof.

Argh!!!

I've been playing around with this and I can't get it...

Here's what I have thus far:

Given [tex]\mid u \cdot v \mid \leq \parallel u \parallel \parallel v \parallel [/tex]

[tex] (u \cdot v)^2 \leq (u_1^2 + u_2^2)(v_1^2 + v_2^2)[/tex]

[tex] (u_1v_1+u_2v_2)^2 \leq (u_1^2 + u_2^2)(v_1^2 + v_2^2)[/tex]

[tex] (u_1v_1+u_2v_2)^2 \leq (u_1^2 + u_2^2)(v_1^2 + v_2^2)[/tex]

[tex]u_1^2v_1^2+u_2^2v_2^2+2u_1v_1u_2v_2 \leq u_1^2v_1^2 + u_2^2v_1^2+u_1^2v_2^2 + u_2^2v_2^2[/tex]

[tex]2u_1v_1u_2v_2 \leq u_2^2v_1^2+u_1^2v_2^2[/tex]

This is where I get stumped which means I messed up somewhere earlier in my proof. Any help here would be greatly appreciated.

Thanks a lot.

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# Homework Help: Help with Cauchy-Schwartz Inequality proof.

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