semi-norm

See also: seminorm

English

Alternative forms

seminorm

Etymology

semi- +‎ norm

Noun

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

(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

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