Combinatorial matrix theory

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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.