Application of Method of Tensor Invariants to the Calculation of Physical Tensors of Crystals——(I) Principles

The method of tensor invariants (MTI) to determine the components of physical tensors is improved and generalized. The principles of MTI and the procedure of its application are elaborated systematically. Based upon the theorems of shadow and the number of independent tesor components, all the isovariant orthogonal bases up to rank 3 for 32 crystal point groups are listed, so the method is easily applied to all cases of physical tensors that in common use.