Results for by Wondratschek, H.
Matrix–column pairs and (n + 1) × (n + 1) matrices
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.4, p.
and are designated by open-face letters in this volume: In order to write equation (1.2.2.3) as with the augmented matrices, the columns and x also have to be extended to the augmented columns and . Equations (1.2.2.5 ...

Coordinate systems and coordinates
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.2, p.
vectors. Definition 1.2.2.2.1.  A basis which consists of lattice vectors of a crystal pattern is called a lattice basis or a crystallographic basis . Referred to a lattice basis, each lattice vector ...

The description of mappings
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.3, p.
or matrix part, the column w is the translation part or column part of a mapping. In equations (1.2.2.1) and (1.2.2.3), the coordinates are mixed with the quantities describing the mapping, designated ...

Isometries
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.5, p.
References Hahn, Th. & Wondratschek, H. (1994). Symmetry of Crystals. Introduction to International Tables for Crystallography, Vol. A . Sofia: Heron Press. Google Scholar International Tables for Crystallography (2005). Vol ...

Vectors and vector coefficients
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.6, p.
. Thus, the column of the coefficients of a vector is not augmented by `1' but by `0'. Therefore, when the point P is mapped onto the point by according to equation (1.2.2.3), then the vector is mapped onto the vector by transforming ...

Origin shift and change of the basis
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.7, p.
according to equations (1.2.2.1) to (1.2.2.3), and the column of vector coefficients is v, see Section 1.2.2.6 . A new coordinate system may be introduced with the basis and the origin . Referred to the new coordinate system ...

Mappings and matrices
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2, p.
: In order to write equation (1.2.2.3) as with the augmented matrices, the columns and x also have to be extended to the augmented columns and . Equations (1.2.2.5) and (1.2.2.6) then become The vertical ...

Crystallographic symmetry operations
Wondratschek, H., International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.1, p.
Definition 1.2.2.1.1.  A mapping is called a motion, a rigid motion or an isometry if it leaves all distances invariant (and thus all angles, as well as the size and shape of an object). In this volume the term `isometry' is used ...