orthonormal transformation

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an orthonormal transformation) preserves lengths of vectors and angles between vectors, 〈v, w〉 = 〈T v, T w〉. In addition, an orthogonal transformation is either a rigid rotation or an improper rotation (a rotation followed by a flip). (Flipping and then rotating can be realized by first rotating in the reverse direction and then flipping.) Orthogonal transformations correspond to and may be represented using orthogonal matrices.

improper rotation | inner product | Lie group | linear transformation | Lorentz transformation | matrix | orthogonal group | orthogonality condition | orthogonal matrix | rotation