Dictionary

semi-norm en · NOUN

Etymology

Etymology tree Proto-Indo-European *sem- Proto-Indo-European *sēmi Latin sēmi-bor. English semi- English norm English semi-norm From semi- + norm.

Meanings

1. 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.

Forms

Deriveds

seminormed · semi-normed

Relateds

norm

Synonyms

gauge (in analysis)

Translations (5)

de Halbnorm (a function that maps a vector to a non-negative value) · de Seminorm (a function that maps a vector to a non-negative value) · it norma (a function that maps a vector to a non-negative value) · sv seminorm (a function that maps a vector to a non-negative value) · bg полунорма (a function that maps a vector to a non-negative value)