semi-norm

semi-norm

See also: seminorm

English

Alternative forms

• seminorm

Etymology

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

Italian: norma (it) f

Swedish: seminorm (sv)

See also

• norm

Anagrams

• misnomer