# semi-norm

Definition from Wiktionary, the free dictionary

## Contents

## English[edit]

### Alternative forms[edit]

### Noun[edit]

**semi-norm** (*plural* **semi-norms**)

- (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.

#### Synonyms[edit]

- (
*in analysis*): gauge