semi-norm

Noun.  (analysis) A function denoted ||''v''|| that maps a vector ''v'' to a non-negative value such that ||''cv''|| = |''c''|.||''v''||, where ''c'' is a scalar, and ||''v'' + ''w''|| ≤ ||''v''|| + ||''w''|| (the triangle inequality); the condition that ||''v''|| = 0 implies that ''v'' = 0 is not required, but when it holds, the semi-norm is a norm.

This is an unmodified, but possibly outdated, definition from Wiktionary and used here under the Creative Commons license. Wiktionary is a great resource. If you like it too, please donate to Wikimedia.

This entry was last updated on RefTopia from its source on 3/20/2012.