Mathematical Sciences: Matrix and Combinatorial Theory

这个项目涉及到矩阵和组合论。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，以及行列式和恒等式的矩阵分解。另一位研究者则与矩阵理论有关。他将致力于非负矩阵、相关的M-矩阵类、矩阵的标度和矩阵的惯性理论。矩阵是一个矩形数组，其中可能包含来自各种环的条目。这是一个起源于九世纪的一个领域，是代数的一部分。它目前非常活跃，因为它的许多应用和与数学和其他科学和技术学科的其他部分的联系。

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.