Orthogonal basis

In mathematics, particularly linear algebra, an orthogonal basis for an inner product space V is a basis for V whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis.

In functional analysis, an orthogonal basis is any basis obtained from a orthonormal basis (or Hilbert basis) using multiplication by nonzero scalars.

Any orthogonal basis can be used to define a system of orthogonal coordinates.

A linear combination of the elements of a basis can be used to reach any point in the vector space, so of course the same property holds in the specific case of an orthogonal basis.

References

• Lang, Serge (2004), Algebra, Graduate Texts in Mathematics 211 (Corrected fourth printing, revised third ed.), New York: Springer-Verlag, pp. 572–585, ISBN 978-0-387-95385-4 
• Milnor, J.; Husemoller, D. (1973). Symmetric Bilinear Forms. Ergebnisse der Mathematik und ihrer Grenzgebiete 73. Springer-Verlag. p. 6. ISBN 3-540-06009-X. Zbl 0292.10016. 

External links

• Weisstein, Eric W., "Orthogonal Basis", MathWorld.