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A generalization of the concept of an absolute value or norm on a field, involving a weakening of one of the axioms: instead of the condition only is required. An example of a pseudo-norm: in the ring of all real-valued continuous functions defined on the segment a pseudo-norm which is not an absolute value is defined by the formula

Every real finite-dimensional algebra can be given a pseudo-norm.


[1] A.G. Kurosh, "Lectures on general algebra" , Chelsea (1963) (Translated from Russian)
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Pseudo-norm. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article