The spectral norm of a nonnegative matrix (Q917654)

The author proves that for any matrix \(A=(a_{ij})\) with \(| A| =(| a_{ij}|)\) it holds that \(\| | A| \|_ 2=\min \{r_ 1(B)\cdot c_ 1(C):\) \(B\circ C=A\}\geq \| A\|_ 2\) and determines the case of equality and the conditions of the uniqueness of minimizers, where \(c_ 1(A)=\max_{j}(\sum_{i}| a_{ij}|^ 2)^{1/2}\) and \(r_ 1(A)=\max_{i}(\sum_{j}| a_{ij}|^ 2)^{1/2}\).