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It is well known that any nonsingular M–matrix admits an LU fac-torization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without(More)
Let A be an M{matrix and B a nonnegative matrix. In this paper it is shown that with some additional constraints, the index of zero for BA is at least as large as the index of zero for A. This result is used to develop properties of splittings of an M{matrix. Weak collapsed graph compatible and collapsed graph compatible splittings are introduced here, and(More)
A complex matrix A is ray{nonsingular if det(X A) 6 = 0 for every matrix X with positive entries. A suucient condition for ray{nonsingularity is that the origin is not in the relative interior of the convex hull of the signed transver-sal products of A. The concept of an isolated set of transversals is deened and used to obtain a necessary condition for A(More)
Sexual harassment law presents a complex set of issues not only for lawyers but also for psychiatrists in their roles both as evaluators and clinicians. Judge Reinhardt of the US Court of Appeals for the 9th Circuit, summed up these complexities: "We tend these days, far more than in earlier times, to find our friends, lovers, and even mates in the(More)
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