International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.2, pp. 67-68

## Section 1.2.7.4.3. Diagonalization of the action matrix and determination of the invariant tensor

M. Ephraïm,b T. Janssen,a A. Jannerc and A. Thiersd

#### 1.2.7.4.3. Diagonalization of the action matrix and determination of the invariant tensor

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An invariant element of the tensor space under the group G is a vector v that is left invariant under each generator: If the number of generators is one, . This equation is solved by diagonalization: where . The dimension of the solution space is the number of elements that are equal to zero. The corresponding rows of Q form a basis for the solution space. (See example further on.)