Coordinate vector

<p>In <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, a coordinate vector is a representation of a <a href="/facts/Vector_(mathematics_and_physics)/U8mM7A5F">vector</a> as an ordered list of numbers (a <a href="/facts/Tuple/BI1HIxL8">tuple</a>) that describes the vector in terms of a particular <a href="/facts/Ordered_basis/89IPoN6c">ordered basis</a>. An easy example may be a position such as (5, 2, 1) in a 3-dimensional <a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinate system</a> 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 <a href="/facts/Vector_space/M1pxMLx2">vector spaces</a> and <a href="/facts/Linear_transformation/Q1PBKNVV">linear transformations</a> concretely as <a href="/facts/Column_vector/pPuRr9Xk">column vectors</a>, <a href="/facts/Row_vector/pPuRr9Xk">row vectors</a>, and <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrices</a>; hence, they are useful in calculations.
</p><p>The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below.
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Coordinate vector open-in-new

Coordinate vector