As far as I remembered there is an inverse Hadamard inequality for the determinant of the form
$$
|D|>\prod\_j \sqrt{(a\_{jj}^2-\sum\_{i\neq j}a\_{ij}^2)}
$$
providing all values in $(\cdot)>0$.


Please help me with exact references to this inequality, its possible generalizations and modifications and comments. 



Inverse Hadamard determinant inequality
Did you mean Ostrowski's theorem $$|D|>\prod\_j \left(|a\_{jj}|-\sum\_{i\neq j}|a\_{ij}|\right)$$
for diagonally dominant matrices (see e.g. <http://planetmath.org/propertiesofdiagonallydominantmatrix>)?


