Category:Point Lattices
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This category contains results about Point Lattices.
Definitions specific to this category can be found in Definitions/Point Lattices.
Definition 1
A point lattice is a discrete subgroup of $\R^m$ under addition.
Definition 2
Let $\R^m$ be the $m$-dimensional real Euclidean space.
Let $\set {\mathbf v_1, \mathbf v_2, \ldots, \mathbf v_n}$ be a linearly independent set of vectors of $\R^m$.
A point lattice in $\R^m$ is the set of all integer linear combinations of such vectors.
That is:
- $\ds \map \LL {\mathbf v_1, \mathbf v_2, \ldots, \mathbf v_n} = \set {\sum_{i \mathop = 1}^n a_i \mathbf v_i : a_i \in \Z}$