semi-norm

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semi-norm

noun semi-norms · seminorm

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.
Similar: gauge

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noun a function that maps a vector to a non-negative value

Deutsch	Halbnorm, Seminorm
Italiano	norma

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MLA

"semi-norm." Wiktionary, via Micwyn, micwyn.com/word/semi-norm. Accessed 6 Nov. 2026.

APA

semi-norm. (n.d.). In Wiktionary, via Micwyn. Retrieved November 6, 2026, from https://micwyn.com/word/semi-norm

Chicago

"semi-norm." Wiktionary, via Micwyn. Accessed November 6, 2026. https://micwyn.com/word/semi-norm.

BibTeX

@misc{semi_norm_2026,
  title = {semi-norm},
  howpublished = {Wiktionary, via Micwyn},
  year = {2026},
  url = {https://micwyn.com/word/semi-norm},
  urldate = {2026-11-06}
}