This award supports work in matrix theory. The principal investigator will seek a better understanding of eigenvalues of (0,1)-matrices, partially ordered sets with the fixed point property, transversal matroids especially those that arise bicircular matroids of graphs, and tree-packing problems and their relation to the joint-realization of (0,1)-matrices with prescribed row and column sums. The co-principal investigator will work on non-negative matrices, the related class of M-matrices and their generalizations, on scaling of matrices and inertia theory of matrices. The work on sparse matrix analysis and the work on scaling of matrices has applications to problems in manufacturing. A matrix is a rectangular array with possible entries from a wide variety of rings. This is a field which originated in the nineteenth century as part of algebra. It is currently very active in view of its many applications and connections with other parts of mathematics as well as other scientific and technical disciplines.
