Improving bounds for eigenvalues of complex matrices using traces Original Research Article

Let A be a complex matrix of order n with eigenvalues image and m be any integer satisfying image. The bound for ∑λj2 by Kress, de Vries, and Wegmann is strengthened. Furthermore, new bounds are presented to estimate the spectral radius of A using m and traces of A, A2, A*A and A*A-AA*. We also improve some Wolkowicz–Styan bounds and previous localization of eigenvalues in rectangular or elliptic regions using traces. Several simple lower bounds for the spectral radius are given, involving image, image, image, and m.