semi-norm
semi-norm noun: 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.
Noun
semi-norm (plural semi-norms)
- 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:
- gauge
Synonyms of semi-norm
Forms of semi-norm
| plural | semi-norms |
|---|---|
| alternative form | seminorm |
Origin of semi-norm
From semi- + norm.
Words formed from semi-norm
- semi-normed
- seminormed
Questions about semi-norm
- What does semi-norm mean?
- Semi-norm means 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 part of speech is semi-norm?
- Semi-norm is a noun.
- What is the plural of semi-norm?
- The plural of semi-norm is semi-norms.
Words near semi-norm in the dictionary
Source and license
Adapted from Wiktionary: semi-norm (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
Last updated:
Cite this entry: “semi-norm.” Word.ws, https://word.ws/semi-norm. Based on Wiktionary, CC BY-SA 4.0.