Orthonormal basis

Common card · No. 302826

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V {\displaystyle V} with finite dimension is a basis for V {\displaystyle V} 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 R n {\displaystyle \mathbb {R} ^{n}} 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 (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for R n {\displaystyle \mathbb {R} ^{n}} arises in this fashion. An orthonormal...

Read on Wikipedia