Some inequalities connecting the singular values of a complex matrix with the Perron roots of related nonnegative matrices

In the paper, some inequalities interrelating the singular values of a square matrix $A$ with complex entries with the Perron roots of the associated nonnegative matrices $P_A=|A|\circ|A|$ and $(P_A+P_A^T)/2$ are derived. The results obtained are applied to $(0,1)$-matrices.