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Similarly, the configuration of uniformly spaced sampling points in one-dimension can be generalized to a [[Lattice (group)|lattice]] in higher dimensions. A lattice is a collection of points <math>\Lambda \subset \Re^n</math> of the form
<math>
\Lambda = \left\{ \sum_{i=1}^n a_i v_i \; | \; a_i \in\
</math>
where {''v''<sub>1</sub>, ..., ''v''<sub>''n''</sub>} is a [[Basis (linear algebra)|basis]] for <math>\Re^n</math>. The [[reciprocal lattice]] <math>\Gamma</math> corresponding to <math>\Lambda</math> is defined by
:<math>
\Gamma = \left\{ \sum_{i=1}^n a_i u_i \; | \; a_i \in\
</math>
where the vectors <math>u_i</math> are chosen to satisfy <math>\langle u_i, v_j \rangle = \delta_{ij}</math>. That is, if the vectors <math>u_i</math> form columns of a matrix <math>A</math> and <math>v_i</math> the columns of a matrix <math>B</math>, then <math>A=B^{-T}</math>. An example of a sampling lattice in two dimensional space is a [[hexagonal lattice]] depicted in Figure 1. The corresponding reciprocal lattice is shown in Figure 2. The reciprocal lattice of a [[square lattice]] in two dimensions is another square lattice. In three dimensional space the reciprocal lattice of a
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