Semi-norm
Definition & Meaning
Part of speech noun
Quick meaning: Semi-norm is a noun meaning (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.
Meaning
(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.
Word Forms
- semi-norms
- seminorm
Synonyms for semi-norm
Depending on context, synonyms include gauge.
Related Words
Related dictionary entries include seminorm, norm, two-norm, gauge, norming, magnitude.
Related Dictionary Tools
Sources & Attribution
FreeDictionaryAPI.com / Wiktionary · Original source · CC BY-SA 4.0
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