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 (BB ) is positive… (More)