Matrix norms

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A matrix-norm is a vector-space-norm with two additional requirements:

$|AB| <= |A||B|, "and"$
$|A| = |A*|.$

A vector-norm $|x|$ induces a matrix-norm by:

$|A| = max{|Ax|/|x| : x != 0}.$

An induced matrix-norm is by definition consistent with its inducing vector-norm

$forall x: |Ax| <= |A||x|.$

Not all matrix-norms are induced by a vector-norm.

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Matrix norm