  Given a lattice $L$, a basis $B$ of $L$ together with its dual $B^*$, the
orthogonality measure $S(B)=\sum_i ||b_i||^2 ||b_i^*||^2$ of $B$ was introduced
by M. Seysen in 1993. This measure is at the heart of the Seysen lattice
reduction algorithm and is linked with different geometrical properties of the
basis. In this paper, we explicit different expressions for this measure as
well as new inequalities.
