Mathematical Sciences: Matrix and Combinatorial Theory

这个项目涉及矩阵和组合理论。其中一名研究人员将研究组合矩阵理论中的问题。他将研究双随机矩阵的多面体，经典不变矩阵的初等因子的确定以及行列式和恒式的矩阵分解。另一个研究者关心的是矩阵理论。他将研究非负矩阵，相关的m矩阵，矩阵的缩放和矩阵的惯性理论。矩阵是一个矩形数组，其中可能的元素来自各种各样的环。这个领域起源于19世纪，是代数的一部分。鉴于它的许多应用以及与数学和其他科学技术学科的其他部分的联系，它目前非常活跃。

This project is concerned with matrix and combinatorial theory. One of the investigators will examine problems in combinatorial matrix theory. He will investigate the polytope of doubly stochastic matrices, determination of the elementary divisors of the classical invariant matrices and matrix factorizations of determinants and permanents. The other investigator is concerned with matrix theory. He will work on non-negative matrices, the related class of M-matrices, scaling of matrices and inertia theory of matrices. A matrix is a rectangular array with possible entries from a wide variety of rings. This is a field which originated in the ninetheenth century as a part of algebra. It is curently very active in view of its many applications and connections with other parts of mathematics and other scientific and technical disciplines.