Sharpening of the inequalities of Schur, Eberlein, Kress and Huang, and new location of eigenvalues
Junliang Wu, Dafei Wang · Journal of Mathematical Inequalities · 2014
Let A = (a i j ) be an n n complex matrix with eigenvalues 1 , 2 , , n . We determine the new upper bounds of n j=1 | j | 2 , which will sharpen Schur, Eberlein, Kress and Huang's inequalities. We also exhibit new methods to locate the eigenvalues of a given complex matrix, which are more exact than those existing in previous literature. Numerical examples are provided to show the effectiveness of our results.