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Mathematics-Online course: Linear Algebra - Basic Structures - Scalar Product and Norm

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)

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  automatically generated 4/21/2005