# Crystallographic basis

### From Online Dictionary of Crystallography

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== Definition == | == Definition == | ||

- | 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. | + | 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 **e _{1}**,

**e**, ... ,

_{2}**e**of the vector space

_{n}**V**is a

^{n}*crystallographic basis*of the vector lattice

**L**if

*every*integral linear combination

**t**=

*u*

^{1}

**e**+

_{1}*u*

^{2}

**e**+ ... +

_{2}*u*

^{n}**e**is a lattice vector of

_{n}**L**. It may or may not be a primitive basis.

## See also

direct lattice

Section 8.1 of *International Tables of Crystallography, Volume A*