# Inverse Hadamard determinant inequality

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.

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)?
• Is the next generalization valid with two pivoted elements: let $(a_1,a_2,a_3,\dots)$ be a line of a determinant with $a_1+a_2>\sum_{k=3}^n a_k$. Is the Ostrowski inequality still valid with a product of \prod(a_1+a_2-\sum_{k=3}^n a_k)\$ -??? – Sergei Apr 18 '16 at 16:46