About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Linear Algebra and Its Applications
Paper
On bounds for eigenvalues of real symmetric matrices
Abstract
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.