International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 
International Tables for Crystallography (2013). Vol. D, ch. 1.2, p. 67

The transformation of the monomial under the matrix is given by the polynomial which is in principle noncommutative. This polynomial can be written as a sum of the monomials in the basis taking into account the eventual (anti)symmetry of and . In this way, basis element (a monomial) is transformed to To each generator of G corresponds such an action matrix M.
The action matrix changes if one considers pseudotensors. In the case of pseudotensors, the previous equation changes to The function Det(g) is just a onedimensional representation of the group G. The determinant is either or .