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Next: Mappings and symmetry operations Up: (IUCr) Matrices, Mappings and Crystallographic Symmetry Previous: Distances and angles

Matrices and determinants

The second chapter deals with matrices and determinants which are essential for the analytical description of crystallographic symmetry. Matrices are mathematical tools which may simplify involved calculations considerably and may make complex formulae transparent. One can introduce them in an abstract way as a formalism and then apply them to many calculations in crystallography. However, it seems to be better first to justify their introduction. Determinants are used for the calculation of the volume, e.g. of a unit cell from the lattice constants, or in the process of inverting a matrix.

Subsections

Mappings and symmetry operations
Motivation
The matrix formalism
Rules for matrix calculations
Determinants
Applications

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