Matrix Analysis in Engineering and Science

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MATRIX ANALYSIS IN ENGINEERING AND SCIENCERoy Mathias and Chi-Kwong LiCollege of William and MaryABSTRACTMatrix analysis finds applications in many fields including control theory, differential equations, economics, electrical engineering, graph theory, numerical analysis, operations research and optimization, psychology, quantum physics, and statistics. However, many researchers in these areas may not be able to use the existing results and proof techniques in matrix analysis to develop their theory effectively because their expertise is not in matrix theory and there is a lack of communication between them and researchers in matrix theory. We have considerable experience in matrix analysis and have developed, adapted, or borrowed many techniques to study the subject. In this project, they plan to develop and apply matrixmethods to different problems that arise from applications. In addition to proving the necessary results we will put them in more general and accessible settings, so that the new results andtechniques can be readily used by non-specialists. Matrix analysis is a basic tool in the physical and social sciences, applied mathematics, statistics and engineering. Matrices are a way of organizing and analyzing data. Sometimes simple results in matrix analysis are all that are needed, however, often one needs rather subtle results. Most scientists and engineers receive an only anintroduction to matrices. We will develop and apply matrix methods to a variety of applied problems and will disseminate our results andtechniques to researchers in these applied areas. Our goal is to advance the boundaries in matrix analysis and equip applied researchers.