Difference between revisions of "Crystallographic basis"
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| − | <Font color="blue"> Base cristallographique </Font>(''Fr'').<Font color="black"> Base cristallografica </Font>(''It'') | + | <Font color="blue"> Base cristallographique </Font>(''Fr''). <Font color="red"> Kristallographische Basis </Font> (''Ge''). <Font color="black"> Base cristallografica </Font>(''It'') |
== 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'''. | + | 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 04:52, 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