Dual lattice

Consider a lattice \(\Lambda \subseteq \mathbb{R}^{d}\). Let \(\Lambda^{*}\) be the dual lattice defined as \[\begin{align} \Lambda^{*} = \{ \lambda \in \mathbb{R}^{d}, \ | \ \langle \lambda,\Lambda\rangle \subseteq \mathbb{Z} \}. \end{align}\]