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Almost skew-symmetric matrices are real matrices whose symmetric parts have rank one. Using the notion of the numerical range, we obtain eigenvalue inequalities and a localization of the spectrum of an almost skew-symmetric matrix. We show that almost skew-symmetry is invariant under principal pivot transformation and inversion, and that the symmetric parts… (More)

In this paper we characterize all nonnegative matrices whose inverses are M{matrices with unipathic digraphs. A digraph is called unipathic if there is at most one simple path from any vertex j to any other vertex k. The set of unipathic digraphs on n vertices includes the simple n{cycle and all digraphs whose underlying undirected graphs are trees (or… (More)

- J. J. McDonald
- 1997

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)

- J J Mcdonald, Schneider, Li Kavanagh
- 1994

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)

- Jenna J McDonald, CRY, Jenna J. McDonald
- 2016

Martin for their patience, honesty, and counsel. I am grateful for our many conversations and will forever hold dear your teachings. Thank you to my fellow graduate students for your solidarity, love, encouragement, inspiration, help, and understanding. It is deeply affecting to be a part of such a kind, talented, and inclusive group of individuals. I would… (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)

- J. J. McDonald
- 2007

This article is devoted to a special class of matrices, namely matrices with cut{points. Such matrices arise in many diierent applications. This paper deals with the spectral properties (index, algebraic and geometric multiplicities, etc.) that matrices of this kind inherit from their quasi{blocks.

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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