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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[edit]

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

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

A quasinormed space (A, \| \cdot \|) is called a quasinormed algebra if the vector space A is an algebra and there is a constant K > 0 such that

\|xy\| \leq K \|x\| \cdot \|y\|

for all x, y \in A.

A complete quasinormed algebra is called a quasi-Banach algebra.

See also[edit]