Difference between revisions of "Basis vector"

Latest revision as of 04:02, 21 January 2009

A basis vector for a vector space is a set of linearly independent vectors where every object in the vector space can be described as a linear combinination of the basis vectors. For instance any position vector in a three-dimensional coordinate system with axis x, y and z can be described as a weighted sum of a vector of unit length in the x-axis, unit length in the y-axis and unit length in the z axis. In this example the weights in the weighted sum are the x, y and z coordinate of the point which is described by the position vector.

There are 3 equivalent three-dimensional systems of basis vectors, popular for use in the physical sciences:

• Cartesian Coordinates, which are defined by projection relative to three intersecting orthogonal axes (axes at right angles to one another) whose common intersection forms an origin point.

• Spherical Coordinates, which are defined by radius and angle relative to a 3 dimensional polar reference frame with a fixed origin point.

• Cylindrical Coordinates, which are defined by projection relative to a central axis with a fixed origin point and by radius and angle within an orthogonal 2-dimensional polar reference frame defined relative to that central axis.

Other three-dimensional systems of basis vectors can be defined as needed. Systems of basis vectors are typically selected on the basis of what is most convenient and/or elegant for the computation method employed.

External Links

Definition of a basis vector from [mathworld].