Mathematical Sciences: Matrix and Combinatorial Theory

这项研究涉及到各种各样的问题， 线性代数 其中一名主要研究人员将研究 零模式和符号对矩阵不变量的依赖性; 由贪婪算法定义的纠错码;整数 由组合定义的类生成的格 矩阵.某些类别的 永久性;以及偏序集与矩阵的关系。另 首席研究员将研究非负矩阵; M-矩阵及其推广; M-矩阵的标度 矩阵;和矩阵的惯性理论。 矩阵是一个矩形数组，其中可能有来自 各种各样的戒指 这是一个起源于 19世纪作为代数的一部分。 它还很 鉴于其众多的应用和联系， 数学和其他科学技术的其他部分 学科

This research is concerned with a variety of problems in linear algebra. One of the principal investigators will study the dependency of zero patterns and signs on matrix invariants; error-correcting codes defined by a greedy algorithm; integer lattices generated by combinatorially defined classes of matrices; computational procedures for certain classes of permanents; and the relation of posets to matrices. The other principal investigator will work on non-negative matrices; the related class of M-matrices and their generalizations; 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 nineteenth century as a part of algebra. It is currently very active in view of its many applications and connections with other parts of mathematics and other scientific and technical disciplines.