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.
Related concepts
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
for all
A complete quasinormed algebra is called a quasi-Banach algebra.