From Online Dictionary of Crystallography
Revision as of 14:43, 20 November 2017 by BrianMcMahon (Added German and Spanish translations (U. Mueller))
Espace vectoriel (Fr). Vektorraum (Ge). Spazio vettoriale (It). ベクトル空間 (Ja). Espacio vectorial (Sp).
For each pair of points X and Y in point space one can draw a vector r from X to Y. The set of all vectors forms a vector space. The vector space has no origin but instead there is the zero vector which is obtained by connecting any point X with itself. The vector r has a length which is designed by |r| = r, where r is a non–negative real number. This number is also called the absolute value of the vector. The maximal number of linearly independent vectors in a vector space is called the dimension of the space.
An essential difference between the behaviour of vectors and points is provided by the changes in their coefficients and coordinates if a different origin in point space is chosen. The coordinates of the points change when moving from one origin to another one. However, the coefficients of the vector r do not change.
- Chapter 1.3.2 of International Tables for Crystallography, Volume A, 6th edition
- Matrices, Mappings and Crystallographic Symmetry (Teaching Pamphlet No. 22 of the International Union of Crystallography)