## Basis

A (vector) basis is any Set of Linearly Independent Vectors capable of generating an -dimensional Subspace of . Given a Hyperplane defined by

a basis is found by solving for in terms of , , , and . Carrying out this procedure,

so

and the above Vector form an (unnormalized) Basis. Given a Matrix A with an orthonormal basis, the Matrix corresponding to a new basis, expressed in terms of the original is

See also Bilinear Basis, Modular System Basis, Orthonormal Basis, Topological Basis

© 1996-9 Eric W. Weisstein
1999-05-26