What does "semi-norm" mean?

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.

What is a synonym for "semi-norm"?

Common synonyms include: gauge.

Semi-norm

noun

noun ·Rare ·Advanced level

Definitions

Noun

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.

Synonyms

All synonyms

gauge

Etymology

From semi- + norm.

Related phrases

semi-normed

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.