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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