ENGLISH DICTIONARY

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

Synonyms for semi-norm

Depending on context, synonyms include gauge.

Related Words

Related dictionary entries include seminorm, norm, two-norm, gauge, norming, magnitude.

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Sources & Attribution

FreeDictionaryAPI.com / Wiktionary · Original source · CC BY-SA 4.0

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