semi-norm

See also: seminorm

English

Alternative forms

• seminorm

Etymology

From semi- +‎ norm.

Noun

semi-norm (plural semi-norms)

1. (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

• (in analysis): gauge

Derived terms

• semi-normed, seminormed

Translations

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

• German: Halbnorm f, Seminorm f
• Italian: norma (it) f
• Swedish: seminorm (sv)

See also

• norm

Anagrams

• misnomer