Equivariant map in the context of Vector norm

⭐ Core Definition: Equivariant map

In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation.

Equivariant maps generalize the concept of invariants, functions whose value is unchanged by a symmetry transformation of their argument. The value of an equivariant map is often (imprecisely) called an invariant.

↓ Menu

Equivariant map in the context of Magnitude (vector)

In mathematics, a norm is a function from a real or complex vector space to the non-negative 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 zero is only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself.

A seminorm satisfies the first two properties of a norm but may be zero for vectors other 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.

View the full Wikipedia page for Magnitude (vector)

↑ Return to Menu

Equivariant map in the context of Vector norm

Equivariant map Study page number 1 of 1

Play TriviaQuestions Online!

Skip to study material about Equivariant map in the context of "Vector norm"

⭐ Core Definition: Equivariant map

Equivariant map in the context of Magnitude (vector)