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单词 norm
释义
norm

Mathematics
  • A norm on a real or complex vector space V is a map ‖.‖:V →ℝ such that (i) ‖v‖ ≥0 for all v and ‖v‖ =  0 if and only if v =  0; (ii) ‖kv‖ =  |k| ‖v‖ for all v and all scalars k; (iii) ‖v + w‖ ≤ ‖v‖ + ‖w‖. Examples include the absolute value of real numbers, modulus of a complex number, p-norms, and matrix norms. The term norm is confusingly used in other contexts: see Euclidean domain, partition (of an interval).


Computer
  • See approximation theory.


Geology and Earth Sciences
  • See cipw norm calculation.


Philosophy
  • A norm is a rule for behaviour, or a definite pattern of behaviour, departure from which renders a person liable to some kind of censure. In this sense there are grammatical norms, and norms of etiquette, as well as moral norms. Indeed, almost all aspects of human behaviour will be to some extent norm-governed. The nature of norms, the source of their authority, and the form they should take, occupy centre-stage in any theory of ethics, philosophy of language, and of law, and they also play at least a major role in distinguishing the human sciences or Geisteswissenschaften from the natural sciences. See also rule-following considerations.


Economics
  • See social custom.


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