Rotations are based on a linear vector space. It is not always Cartesian or non-orthogonal. The determinants are 1 and each matrix element is 0, 1 or -1 in crystal.

Second class tensor can be rotated by similarity transformation, e.g., in Cartesian coordinate. Prior to use the reduced rotations, they are transformed to those in Cartesian coordinate and the transformations are written as,

(3.23) |

where, is a cell axes matrix and is represented in oblique coordinates. Then the force constants matrix is transfered. In the case of similarity transformation, the transformation is written as,

(3.24) |

togo 2009-02-12