# Proof for Vectors

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Prove for any two vectors |alpha > and |beta>,

Let a = alpha and b = beta

Prove for any two vectors |a> and |b>,

(<a|a>^(1/2) + <b|b>^1/2)^2 greater than or equal to (<a| + <b|)(|a> + |b>)

Use the Schwartz inequality.

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#### Solution Preview

(<a|a>^(1/2) + <b|b>^1/2)^2 = <a|a> + <b|b> + 2(<a|a>.<b|b>)^1/2 = <a|a> + <b|b> + 2 |a| .|b|

(<a| + ...

#### Solution Summary

Using Schwartz, inequality, a vector identity is proved in the solution.

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