Crystallographic basis

From Online Dictionary of Crystallography

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== Definition ==
== Definition ==
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A basis of ''n'' vectors '''e<sub>1</sub>''', '''e<sub>2</sub>''', ... , '''e<sub>n</sub>''' of the vector space '''V<sup>n</sup>''' is a ''crystallographic basis'' of the vector lattice '''L''' if ''every'' integral linear combination '''t''' = ''u''<sup>1</sup>'''e<sub>1</sub>''' + ''u''<sup>2</sup>'''e<sub>2</sub>''' + ... + ''u<sup>n</sup>'''''e<sub>n</sub>''' is a lattice vector of '''L'''. It may or may not be a primitive basis.
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A basis of ''n'' vectors '''e<sub>1</sub>''', '''e<sub>2</sub>''', ... , '''e<sub>n</sub>''' of the vector space '''V<sup>n</sup>''' is a ''crystallographic basis'' of the vector lattice '''L''' if ''every'' integral linear combination '''t''' = ''u''<sup>1</sup>'''e<sub>1</sub>''' + ''u''<sup>2</sup>'''e<sub>2</sub>''' + ... + ''u<sup>n</sup>'''''e<sub>n</sub>''' is a lattice vector of '''L'''. It may or may not be a [[primitive basis]].
== See also ==
== See also ==

Revision as of 05:06, 5 May 2006

Base cristallographique (Fr). Kristallographische Basis (Ge). Base cristallografica (It)


Definition

A basis of n vectors e1, e2, ... , en of the vector space Vn is a crystallographic basis of the vector lattice L if every integral linear combination t = u1e1 + u2e2 + ... + unen is a lattice vector of L. It may or may not be a primitive basis.

See also

direct lattice
Section 8.1 of International Tables of Crystallography, Volume A