Most of the part inside code, the coordinate system is represented by
reduced coordinates but Cartesian coordinates. The reduced and
Cartesian coordinates are related by cell parameters. Force constants
are treated in Cartesian coordinates. Therefore the eigenvectors are
given in Cartesian.
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,
is a cell axes matrix and
represented in oblique coordinates. Then the force constants
is transfered. In the case of similarity
transformation, the transformation is written as,