Euclidean vector space

1 Definition

The term Euclidean vector space is synonymous with finite-dimensionalPlanetmathPlanetmath, real, positive definitePlanetmathPlanetmath, inner product spaceMathworldPlanetmath. The canonical example is n, equipped with the usual dot productMathworldPlanetmath. Indeed, every Euclidean vector space V is isomorphic to n, up to a choice of orthonormal basisMathworldPlanetmath of V. As well, every Euclidean vector space V carries a natural metric space structure given by


2 Remarks.

Title Euclidean vector space
Canonical name EuclideanVectorSpace
Date of creation 2013-03-22 15:38:24
Last modified on 2013-03-22 15:38:24
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 9
Author rmilson (146)
Entry type Definition
Classification msc 15A63
Related topic InnerProductSpace
Related topic UnitarySpace
Related topic PositiveDefinite
Related topic EuclideanDistance
Related topic Vector
Related topic EuclideanVectorSpace