Euclidean space

Metadata
shorthands: {}
aliases: [Euclidean vector space]
created: 2021-12-13 16:47:26
modified: 2022-01-10 04:13:03

A Euclidean vector space is a finite dimensional inner product space over the field of real numbers.

A Euclidean space is an affine space over the real numbers such that the associated vector space is a Euclidean vector space.

Vector space

The vector space associated to a Euclidean space is an inner product space.

The inner product of a Euclidean space is often called dot product and denoted .


Norm

The Euclidean norm of a vector is:

Distance

The distance of point and :