# semi-norm

Jump to navigation
Jump to search

*See also:*

**seminorm**

## English[edit]

### Alternative forms[edit]

### Etymology[edit]

### Noun[edit]

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

- (mathematical 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

#### Derived terms[edit]

#### Translations[edit]

a function that maps a vector to a non-negative value