Well, I have solved this problem from a textbook:(adsbygoogle = window.adsbygoogle || []).push({});

Prove the Schwarz inequality.

When you try to solve it, you wonder - how do i begin? But thankfully, the problem had a hint: Let [itex]\left|γ\right\rangle = \left|β\right\rangle - \frac{\left\langleα\right| \left|β\right\rangle}{\left\langleα\right| \left|α\right\rangle} \left|α\right\rangle[/itex], and use [itex]\left\langleγ\right| \left|γ\right\rangle \geq 0[/itex].

Well, with this hint, the problem becomes a piece of cake. But how would you know where to start if you didn't have the hint? That's the problem - the starting point. Any ideas?

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# Proving Schwarz inequaltiy - how to begin

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