Quasinorm

In linear algebra, functional analysis and related areas of mathematics, a quasinorm is similar to a norm in that it satisfies the norm axioms, except that the triangle inequality is replaced by:$|x\; +\; y|\; leq\; K(|x|\; +\; |y|)$for some $K\; >\; 1.$

This is not to be confused with a seminorm or pseudonorm, where the norm axioms are satisfied except for positive definiteness.

Related concepts

A vector space with an associated quasinorm is called a quasinormed vector space.

A complete quasinormed vector space is a quasi-Banach space.

See also

*Seminorm

References

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