BOUNDS FOR THE SPECTRUM OF NORMAL MATRICES

Let A be a normal matrix with eigenvalues lambda1, lambda2, ..., lambd a(n), and let GAMMA denote the smallest disc containing these eigenval ues. We give some inequalities relating the center and radius of GAMMA to the entries in A. When applied to Hermitian matrices our results g ive lower bounds on the spread max(ij) (lambda(i) - lambda(j)) of A. W hen applied to positive definite Hermitian matrices they give lower bo unds on the Kantorovich ratio max(ij)(lambda(i) - lambda(j))/(lambda(i ) + lambda(j)).