Any linear transformation

satisfying the Orthogonality Condition

where Einstein Summation has been used and is the Kronecker Delta, is called an orthogonal transformation.

Orthogonal transformations correspond to rigid Rotations (or Rotoinversions), and may be represented using Orthogonal Matrices. If is an orthogonal transformation, then .

**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.

© 1996-9

1999-05-26