Definition:Point Lattice/Definition 2

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Definition

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:

$\ds \map \LL {\mathbf v_1, \mathbf v_2, \ldots, \mathbf v_n} = \set {\sum_{i \mathop = 1}^n a_i \mathbf v_i : a_i \in \Z}$


Also known as

A point lattice is also known just as a lattice, but that term has more than one meaning.

Hence point lattice is what is to be used on $\mathsf{Pr} \infty \mathsf{fWiki}$ for this concept.


Also see

  • Results about point lattices can be found here.


Sources