Mathematics-Online lexicon: Cauchy-Schwarz Inequality

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	Mathematics-Online lexicon:
	Cauchy-Schwarz Inequality

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The scalar product can be estimated by the associated norm:

$\displaystyle \vert\langle u,v \rangle\vert \le \vert u\vert\vert v\vert,\quad \vert w\vert = \sqrt{\langle w,w\rangle}\, .$

We have equality if and only if $u\parallel v$ .

(Authors: Burkhardt/Höllig/Hörner)

see also:

automatically generated 3/15/2005