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Let A be a nonsingular matrix with positive inverse and B a nonnegative matrix. Let the inverse of A + vB be positive for 0 < v < v < +00 and at least one of its entries be equal to zero for v = v* ; an algorithm to compute v* is described in this paper. Furthermore, it is shown that if A + A is positive definite, then the inverse of A + v (B-B ) is positive for 0 < v < v* .doi:10.1090/s0025-5718-1990-0995208-2 fatcat:g7b7cutjcjcl3kklpern2ssnjq