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
; Symmetry operation; motion
(W, w) Symmetry operation , described by an matrix W and an column w
Symmetry operation , described by an augmented' matrix
I unit matrix
Translation
(I, t) Translation , described by the unit matrix I and an column t
Translation , described by an augmented' matrix
Identity operation
(I, o) Identity operation , described by the unit matrix I and the column o
Identity operation , described by the augmented' unit matrix
, or Position vector (of a point or an atom), described by an augmented' column
(P, p); or (S, s) Transformation of the coordinate system, described by an matrix P or S and an column p or s
; or Transformation of the coordinate system, described by an `augmented' matrix
(Q, q) Inverse transformation of (P, p)
Inverse transformation of