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 orthogonal basis can be used to reach any point in the vector space.

See also

• Basis (linear algebra)
• Orthonormal basis

References

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

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