Unimodular lattice

A lattice $ L $ in $ \mathbf R ^ {n} $ such that $ \mathop{\rm vol} ( \mathbf R ^ {n} \mid L) = 1 $. If $ a _ {1} \dots a _ {n} $ are $ n $ vectors in $ \mathbf R ^ {n} $, then the lattice spanned by $ a _ {1} \dots a _ {n} $ is unimodular if and only if $ | \mathop{\rm det} ( a _ {1} \dots a _ {n} ) | = 1 $( because $ \mathop{\rm vol} ( \mathbf R ^ {n} \mid L ( a _ {1} \dots a _ {n} )) = | \mathop{\rm det} ( a _ {1} \dots a _ {n} ) | $).

References

[a1]	J. Milnor, D. Husemoller, "Symmetric bilinear forms" , Springer (1973) pp. 16