** Next:** 3.3 Calculation of the reciprocal lattice
**Up:** 3. Reciprocal Space and Dual Space
** Previous:** 3.1 Definition

Let *V* be the volume of the unit cell. In a change of coordinate:

(3.9) |

(3.10) |

Let us now assume that the base **e**_{j} is orthonormal. There comes:

(3.11) |

We have then demonstrated the following general result:

(3.12) |

From (3.6) we know that

(3.13) |

It is easy to show the following relation, equivalent to (3.12):

(3.14) |

From (3.12), (3.13) and (3.14), we obtain finally:

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