In linear algebra, a coordinate vector is an explicit representation of a Euclidean vector in an abstract vector space as an ordered list of numbers or, equivalently, as an element of the coordinate space Fn. Coordinate vectors allow calculations with abstract objects to be transformed into calculations with blocks of numbers (matrices, column vectors and row vectors).
The idea of a coordinate vector can also be used for infinite dimensional vector spaces, as addressed below.
Read more about Coordinate Vector: Definition, The Standard Representation, Basis Transformation Matrix, Infinite Dimensional Vector Spaces