Definition:Lattice (Group Theory)/Definition 2

Definition
Let $\R^m$ be the $m$-dimensional real Euclidean space.

Let $\set {b_1, b_2, \ldots, b_n}$ be a set of linearly independent vectors of $\R^m$.

A lattice in $\R^m$ is the set of all integer linear combinations of such vectors.

That is:


 * $\ds \map \LL {b_1, b_2, \ldots, b_n} = \set {\sum_{i \mathop = 1}^n x_i b_i : x_i \in \Z}$

Also see

 * Equivalence of Definitions of Lattices in Group Theory