An orthogonal transformation is a linear transformation
which preserves a symmetric inner product.
In particular, an orthogonal transformation (technically, an orthonormal transformation)
preserves lengths of vectors and angles between vectors,
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.