Gersgorin Variations II: On Themes of Fan and Gudkov

Assume is a family of nonnegative functions of n - 1 nonnegative variables such that, for every matrix A of order n, (moduli of off-diagonal entries in row i of A) for all i implies A nonsingular. We show that there is a positive vector x, depending only on F, such that for all A = and all i, This improves a theorem of Ky Fan [F], and yields a generalization of a non-singularity criterion of Gudkov [Gu].

By: Alan J. Hoffman

Published in: RC22897 in 2003


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