Let $G\in\Bbb R^{n\times k}$ where $k\in\{1,\dots,n\}$ be generator of a lattice $\mathcal L\subsetneq\Bbb R^n$ of rank $r\leq k$ (that is $G$ has rank $r$).
That is $\mathcal L=\{y\in\Bbb R^n:\exists x\in\Bbb Z^k\mbox{ with }y=Gx\}$.
What is the generator and rank of dual lattice?