Improving the localization of eigenvalues for complex matrices
Let \(\lambda_i, i= 1,\dots,n\) denote the spectrum of a complex \(n\)-by-\(n\) matrix \(A\). Several well-known bounds for \(\sum|\lambda_i|^2\) in terms of \(\mathrm{tr}(A), \|A\|, \|AA^*-A^*A\|\) are stated. Generalizations to \(\mathrm{Re}(A)\) and \(\mathrm{Im}(A)\) lead to rectangles containing the spectrum of \(A\). Two examples of order 3 are given.
scientific article; zbMATH DE number 6054566