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.

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

**Copyright © 2002 International Union of
Crystallography**