Abstract
Even though the descriptive definition of orientation is the same in both settings, the explicitnotation of a crystallographic orientation as (3 3) matrix in terms of Euler angles featuredby the popular MATLAB toolbox MTEX differs by an inversion from the quasi-standard notation datedback to the early days of quantitative texture analysis championed by H.-J. Bunge. The origin of thisdiscrepancy is revealed by an enlightening view provided in algebraic terms of a change of basis.Understanding the effect of inversion is instrumental to do proper computations with crystallographicorientations and rotations, e.g. when multiplying with elements of a crystallographic symmetry group,and to compare results of texture analyses accomplished in different settings.
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