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Mathematics-Online lexicon: Annotation to

Matrix Norm

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The matrix norm associated with a vector norm is given by

$\displaystyle \Vert A\Vert = \sup_{x\ne 0}\frac{\Vert Ax\Vert}{\Vert x\Vert} = \max_{\Vert x\Vert=1} \Vert Ax\Vert\, . $

In addition to the norm properties (positivity, homogeneity, subadditivity) we have

$\displaystyle \Vert AB\Vert \le \Vert A\Vert\Vert B\Vert\, , $

that is, the associated matrix norm is submultiplicative.

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  automatisch erstellt am 19.  8. 2013