On bounds for eigenvalues of real symmetric matrices

Let A=(aij) be a real symmetric matrix of order n. We characterize all nonnegative vectors x=(x1,...,xn) and y=(y1,...,yn) such that any real symmetric matrix B=(bij), with bij=aij, i≠jhas its eigenvalues in the union of the intervals [bij-yi, bij+ xi]. Moreover, given such a set of intervals, we derive better bounds for the eigenvalues of B using the 2n quantities {bii-y, bii+xi}, i=1,..., n. © 1981.