\begin{definition}[Definition:Lattice (Group Theory)/Definition 2]
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:
:$\ds \map \LL {b_1, b_2, \ldots, b_n} = \set {\sum_{i \mathop = 1}^n x_i b_i : x_i \in \Z}$
\end{definition}