Orthogonal Transformation
Any linear transformation
 |  |  | |
 | |  | |
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satisfying the Orthogonality Condition
where Einstein Summation has been used and
is the Kronecker Delta, is called an orthogonaltransformation.Orthogonal transformations correspond to rigid Rotations (or Rotoinversions), andmay be represented using Orthogonal Matrices. If 
is an orthogonaltransformation, 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.
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