Combinatorial matrix theory

这项拟议的研究探索了两个不同的数学领域，即图论和代数之间的相互作用。就像生物学家可能研究有机体和有机体各组成部分之间的相互关系一样，我的研究探索了图形和矩阵各组成部分之间的联系。正在探索的一种特殊类型的问题是，数字数组上的数学如何受到定性信息的影响，以及数组中正、负和零条目的模式。有时，此信息本身会限制结果，而与数组中各个数字的大小无关。这项研究是纯数学的典型，并不关注任何特定的应用，只是探索理论及其抽象对象的错综复杂。然而，其中涉及的一些数学确实源于电信、统计设计理论和动力系统中的问题。

The proposed research explores the interplay between two different areas of mathematics, namely graph theory and algebra. As a biologist might study an organism and the interelationship of component parts of the ogranism, my research explores connections between the components of graphs and matrices. One particular type of problem being explored is how mathematics on arrays of numbers is affected by qualitative information, by the pattern of postive, negative and zero entries in the array. Sometimes this information alone restricts results independently of the magnitude of the individual numbers in the array. Typical of pure mathematics, this research is not focusing on any particular application, merely exploring the intricacies of the theory and its abstract objects. Some of the mathematics involved however did arise out of problems in telecommunications, statstical desgin theory and dynamical systems.