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.
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.