The only change is that the indexing set for the coordinates is not finite. The elements of V are finite linear combinations of elements in the basis, which give rise to unique coordinate representations exactly as described before. After an order is chosen, the basis can be considered an ordered basis. If the dimension is κ, then there is some basis of κ elements for V. Suppose V is an infinite-dimensional vector space over a field F. Let V be a vector space of dimension n over a field F and letī = Infinite-dimensional vector spaces

The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below. Bases and their associated coordinate representations let one realize vector spaces and linear transformations concretely as column vectors, row vectors, and matrices hence, they are useful in calculations. Coordinates are always specified relative to an ordered basis. 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. In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. JSTOR ( February 2009) ( Learn how and when to remove this template message).Unsourced material may be challenged and removed.įind sources: 'Coordinate vector' – news Please help improve this article by adding citations to reliable sources. This article needs additional citations for verification.

Change of basis matrix