Mathematical Sciences: Matrix and Combinatorial Theory

本研究涉及线性代数中的各种问题。主要研究人员之一将研究零模式和符号对矩阵不变量的依赖性；贪心算法定义的纠错码；由组合定义的矩阵类生成的整数格；某类永久物的计算过程；以及偏序集和矩阵的关系。另一位首席研究员将研究非负矩阵；m -矩阵的相关类及其推广；矩阵的标度；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 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.