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
for some
This is not to be confused with a seminorm or pseudonorm, where the norm axioms are satisfied except for positive definiteness.
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 is called a quasinormed algebra if the vector space A is an algebra and there is a constant K > 0 such that
for all .
A complete quasinormed algebra is called a quasi-Banach algebra.