coordinate vector (original) (raw)

Let V be a vector space of dimension 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,…,ξn∈K. The n-tuplet (http://planetmath.org/OrderedTuplet) (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).