International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 1.1, p. 10
Section 1.1.3.8.2. Generalization
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Institut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France |
Consider a field of tensors that are functions of space variables. In a change of coordinate system, one has Differentiate with respect to : It can be seen that the partial derivatives behave under a change of axes like a tensor of rank 3 whose covariance has been increased by 1 with respect to that of the tensor . It is therefore possible to introduce a tensor of rank 1, (nabla), of which the components are the operators given by the partial derivatives .