# Coordinate vector

In

linear algebra, a

**coordinate vector** is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular

ordered basis. Coordinates are always specified relative to an ordered basis. Bases and their associated coordinate representations let one realize

vector spaces and

linear transformations concretely as

column vectors,

row vectors, and

matrices, hence are useful in calculations.

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

Let *V* be a vector space of dimension *n* over a field *F* and let

be an ordered basis for *V*. Then for every $v\in V$ there is a unique linear combination of the basis vectors that equals *v*:

The **coordinate vector** of *v* relative to *B* is the sequence of coordinates

This is also called the *representation of v with respect of B*, or the *B representation of v*. The α-s are called the *coordinates of v*. The order of the basis becomes important here, since it determines the order in which the coefficients are listed in the coordinate vector.

This page was last edited on 8 December 2017, at 01:28.

Reference:

https://en.wikipedia.org/wiki/Coordinate_vector under CC BY-SA license.

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