\begin{definition}[Definition:Hermite Constant]
Let $n \in \N$ be a natural number.
Let $L$ be an integer lattice in Euclidean space $R^n$ unit covolume.
That is:
:$\map {\operatorname {vol} } {\dfrac {R^n} L} = 1$
Let $\map {\lambda_1} L$ denote the least length of a nonzero element of $L$.
Let $\sqrt {\gamma_n}$ be the maximum of $\map {\lambda_1} L$ over all such integer lattices $L$.
The '''Hermite constant of dimension $n$''' is the constant $\gamma_n$.
{{NamedforDef|Charles Hermite|cat = Hermite}}
\end{definition}