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

International Tables for Crystallography (2006). Vol. A, ch. 5.1, p. 78

## Section 5.1.2. Matrix notation

H. Arnolda

aInstitut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany

### 5.1.2. Matrix notation

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Throughout this volume, matrices are written in the following notation:

As () row matrices:
(a, b, c) the basis vectors of direct space
(h, k, l) the Miller indices of a plane (or a set of planes) in direct space or the coordinates of a point in reciprocal space
As () or () column matrices:
the coordinates of a point in direct space
the basis vectors of reciprocal space
() the indices of a direction in direct space
the components of a shift vector from origin O to the new origin O
the components of an inverse origin shift from origin O′ to origin O, with
the translation part of a symmetry operation in direct space
the augmented column matrix of the coordinates of a point in direct space
As () or () square matrices:
linear parts of an affine transformation; if P is applied to a row matrix, Q must be applied to a column matrix, and vice versa
W the rotation part of a symmetry operation in direct space
the augmented affine trans-formation matrix, with
the augmented affine trans-formation matrix, with
the augmented matrix of a symmetry operation in direct space (cf. Chapter 8.1 and Part 11 ).