Definition:Lattice (Group Theory)/Definition 2

Definition
Let $\R^m$ be the $m$-dimensional Euclidean space and $\left\{b_1, b_2, ..., b_n\right\}$ 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:


 * $\displaystyle \mathcal L (b_1, b_2, ..., b_n) = \left\{ {\sum_{i \mathop = 1}^n x_i b_i : x_i \in \Z}\right\}$