Norm (mathematics)

Norm (mathematics), Length in a vector space.

In mathematics, a norm is a function from a real or complex vector space to the nonnegative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the Euclidean norm, or 2-norm, which may also be defined as the square root of the inner product of a vector with itself. A pseudonorm or seminorm satisfies the first two properties of a norm, but may be zero for other vectors than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a seminormed vector space.

Matrix norm
6 months ago

Matrix norm ... In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions). Given a field K {\displaystyle...

Operator norm
6 months ago

Operator norm ... In mathematics, the operator norm is a means to create an idea of size for certain linear operators. Formally, it is a norm defined on the space of bounded...

T-norm
5 months ago

T-norm ... In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric...

Uniform norm
6 months ago

Uniform norm ... In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f defined on a set S the non-negative number...

Normed vector space
6 months ago

Normed vector space ... In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers, on which a norm is defined. A norm is the formalization...

Norm
5 months ago

Norm ... speakers frequently refer Norm (mathematics), a map that assigns a length or size to a mathematical object, including: Vector norm, a map that assigns a length...

Absolute value
6 months ago

Absolute value ... is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. In 1806, Jean-Robert Argand introduced...

Social norm
6 months ago

Social norm ... Social norms are shared expectations of acceptable behavior by groups. Social norms can both be informal understandings that govern the behavior of members...

Lp space
6 months ago

Lp space ... In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are...

Euclidean space
6 months ago

Euclidean space ... was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any nonnegative integer dimension, including...

Seminorm
6 months ago
Taxicab geometry
6 months ago
Polarization identity
5 months ago
Ball (mathematics)
6 months ago
Magnitude
5 months ago
Magnitude (mathematics)
6 months ago
Scalar (mathematics)
4 months ago
Field norm
4 months ago
Hermitian adjoint
6 months ago
This article is copied from an article on Wikipedia® - the free encyclopedia created and edited by its online user community. This article is distributed under the terms of GNU Free Documentation License.