Bounds for the spectral radius and the largest singular value (Q1806565)

The authors give a lower bound on the spectral radius and the largest singular value of a square matrix \({\mathbf A}\) in terms of traces of powers of \({\mathbf A}\) and the order of \({\mathbf A}\). As a corollary, the authors get some conditions on regularity of \({\mathbf A}\) and estimates of the rank of \({\mathbf A}\).