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In mathematics, particularly linear algebra, an orthonormal basis for an inner product space with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The image of the standard basis under a rotation or reflection is also orthonormal, and every orthonormal basis for arises in this fashion.
An orthonormal basis can be derived from an orthogonal basis via normalization.
The choice of an origin and an orthonormal basis forms a coordinate frame known as an orthonormal frame.
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