coordinate vector

Let V be a vector spaceMathworldPlanetmath of dimensionPlanetmathPlanetmath n over a field K.  If  (b1,,bn)  is a basis of V, then any element v of V can be uniquely expressed in the form


with  ξ1,,ξnK.  The n-tuplet (  (ξ1,,ξn) is called the coordinate vector of v with respect to the basis in question.  The scalars ξi are the coordinates (or the components of v).

It’s evident that the correspondence


provides a linear isomorphism between the vector space V and the vector space formed by the Cartesian product Kn.

Title coordinate vector
Canonical name CoordinateVector
Date of creation 2013-03-22 19:02:16
Last modified on 2013-03-22 19:02:16
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 6
Author pahio (2872)
Entry type Definition
Classification msc 15A03
Related topic ListVector
Defines coordinates
Defines components