Editing Coordinate vector (section)

{{Short description|Concept in linear algebra}}
{{more citations needed|date=February 2009}}

In [[linear algebra]], a '''coordinate vector''' is a representation of a [[vector (mathematics and physics)|vector]] as an ordered list of numbers (a [[tuple]]) that describes the vector in terms of a particular [[ordered basis]].<ref name="AntonRorres2010">{{cite book|author1=Howard Anton|author2=Chris Rorres|title=Elementary Linear Algebra: Applications Version|url=https://books.google.com/books?id=1PJ-WHepeBsC&q=%22Coordinate+vector%22|date=12 April 2010|publisher=John Wiley & Sons|isbn=978-0-470-43205-1}}</ref> An easy example may be a position such as (5, 2, 1) in a 3-dimensional [[Cartesian coordinate system]] with the basis as the axes of this system. Coordinates are always specified relative to an ordered basis. Bases and their associated coordinate representations let one realize [[vector space]]s and [[linear transformation]]s concretely as [[column vector]]s, [[row vector]]s, and [[matrix (mathematics)|matrices]]; hence, they are useful in calculations.

The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below.