Meanings
nounsemi-norm (plural semi-norms)
plural semi-norms · alternative seminorm
- mathematical analysisA 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: gauge
Synonyms & antonyms
nounA 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.
Similar
Origin
- Proto-Indo-European*sem-
- Proto-Indo-European*sēmi
- Latinsēmi-
- Englishsemi-
- Englishnorm
- Englishsemi-norm
Translations
Bulgarian полунорма
- полунорма (polunorma)a function that maps a vector to a non-negative value
German Halbnorm, Seminorm
- Halbnorma function that maps a vector to a non-negative value
- Seminorma function that maps a vector to a non-negative value
Italian norma
- normaa function that maps a vector to a non-negative value
Swedish seminorm
- seminorma function that maps a vector to a non-negative value
Cite this entry
APA
semi-norm. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/semi-norm
MLA
“semi-norm.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/semi-norm. Accessed November 3, 2026.
Chicago
WatkinsX Dictionary, s.v. “semi-norm,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/semi-norm.
Source: semi-norm on Wiktionary, CC BY-SA 4.0.