Bounds for eigenvalues using the trace and determinant (Q1369286)

The authors consider a square matrix of order \(n\) with real positive eigenvalues \(\lambda_1\geq\cdots\geq \lambda_n>0\) and get lower and upper bounds for products \(\lambda_k\cdot\cdots\cdot \lambda_l\) and sums \(\lambda_k+\cdots+ \lambda_l\) of eigenvalues by using the trace and the determinant as well as of the numbers \(n\), \(k\) and \(l\). In some cases bounds of \textit{H. Wolkowicz} and \textit{G. P. H. Styan} [ibid. 29, 471-506 (1980; Zbl 0435.15015)] could be improved.