Difference between revisions of "Lattice"
From Online Dictionary of Crystallography
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| − | <Font color="blue">Réseau</Font>(''Fr'') | + | <Font color="blue">Réseau</Font>(''Fr''). <Font color="red">Gitter</Font> (''Ge''). <Font color="black">Reticolo</Font>(''It''). <font color="purple">格子</font> (''Ja''). |
| + | A '''lattice''' in the vector space '''V'''<sup>''n''</sup> is the set of all integral linear combinations '''t''' = ''u''<sub>1</sub>'''a<sub>1</sub>''' + ''u''<sub>2</sub>'''a<sub>2</sub>''' + ... + ''u''<sub>k</sub>'''a<sub>k</sub>''' of a system ('''a<sub>1</sub>''', '''a<sub>2</sub>''', ... , '''a<sub>k</sub>''') of linearly independent vectors in '''V'''<sup>''n''</sup>. | ||
| − | + | If ''k = n'', ''i.e.'' if the linearly independent system is a '''basis''' of '''V'''<sup>''n''</sup>, the lattice is often called a '''full lattice'''. In crystallography, lattices are almost always full lattices, therefore the attribute 'full' is usually suppressed. | |
| − | |||
| − | If ''k = n'', i.e. if the linearly independent system is a '''basis''' of '''V<sup>n</sup> | ||
== See also == | == See also == | ||
| − | *[[ | + | *[[Crystallographic basis]] |
| − | * | + | *Chapters 1.3.2 and 3.1 of ''International Tables for Crystallography, Volume A'', 6th edition |
| − | [[Category:Fundamental crystallography]] | + | [[Category:Fundamental crystallography]] |
Revision as of 14:35, 15 May 2017
Réseau(Fr). Gitter (Ge). Reticolo(It). 格子 (Ja).
A lattice in the vector space Vn is the set of all integral linear combinations t = u1a1 + u2a2 + ... + ukak of a system (a1, a2, ... , ak) of linearly independent vectors in Vn.
If k = n, i.e. if the linearly independent system is a basis of Vn, the lattice is often called a full lattice. In crystallography, lattices are almost always full lattices, therefore the attribute 'full' is usually suppressed.
See also
- Crystallographic basis
- Chapters 1.3.2 and 3.1 of International Tables for Crystallography, Volume A, 6th edition