Norms (mathematics)

nonnegative number with the same magnitude as a given real number

generalization of Euclidean geometry to higher-dimensional vector spaces

length in a vector space

type of metric geometry

norm on a vector space of matrices

map that assigns a length or size to any operator in a function space

In mathematics, particularly in functional analysis, a seminorm is like a norm but need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm is the Minkowski functional of some absorbing disk and, conversely, the Minkowski functional of any such set is a seminorm.

p-norm for p equal to ∞

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.