Any linear transformation
Orthogonal transformations correspond to rigid Rotations (or Rotoinversions), and may be represented using Orthogonal Matrices. If is an orthogonal transformation, then .
See also Affine Transformation, Orthogonal Matrix, Orthogonality Condition, Rotation, Rotoinversion
References
Goldstein, H. ``Orthogonal Transformations.'' §4-2 in Classical Mechanics, 2nd ed.
Reading, MA: Addison-Wesley, 132-137, 1980.
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 104, 1993.