International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 1.1, p. 3

Section 1.1.6. Motions and matrices

Th. Hahna*

aInstitut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

1.1.6. Motions and matrices

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Printed symbolExplanation
[{\sf W}]; [{\sf M}] Symmetry operation; motion
(W, w) Symmetry operation [ {\sf W}], described by an [(n \times n)] matrix W and an [(n \times 1)] column w
[\specialfonts{\bbsf W}] Symmetry operation [ {\sf W}], described by an [(n + 1) \times (n + 1)] `augmented' matrix
I [(n \times n)] unit matrix
[ {\sf T}] Translation
(I, t) Translation [ {\sf T}], described by the [(n \times n)] unit matrix I and an [(n \times 1)] column t
[\specialfonts{\bbsf T}] Translation [ {\sf T}], described by an [(n + 1) \times (n + 1)] `augmented' matrix
[ {\sf I}] Identity operation
(I, o) Identity operation [ {\sf I}], described by the [(n \times n)] unit matrix I and the [(n \times 1)] column o
[\specialfonts{\bbsf I}] Identity operation [ {\sf I}], described by the [(n + 1) \times (n + 1)] `augmented' unit matrix
[\specialfonts{\bbsf r}], or [\specialfonts{\bbsf x}] Position vector (of a point or an atom), described by an [(n + 1) \times 1] `augmented' column
(P, p); or (S, s) Transformation of the coordinate system, described by an [(n \times n)] matrix P or S and an [(n \times 1)] column p or s
[\specialfonts{\bbsf P}]; or [\specialfonts{\bbsf S}] Transformation of the coordinate system, described by an [(n + 1) \times (n + 1)] `augmented' matrix
(Q, q) Inverse transformation of (P, p)
[\specialfonts{\bbsf Q}] Inverse transformation of [\specialfonts{\bbsf P}]








































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