Pseudo-norm
From Encyclopedia of Mathematics
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.
References
| [1] | A.G. Kurosh, "Lectures on general algebra" , Chelsea (1963) (Translated from Russian) |
How to Cite This Entry:
Pseudo-norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-norm&oldid=48348
Pseudo-norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-norm&oldid=48348
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article