Spectral analysis of sign/zero-nonzero patterns, positivity of principal minors and primitive diagraphs

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My research primarily concerns combinatorial matrix analysis, in which combinatorial methodology is used to solve and better understand matrix-theoretic problems. The use of combinatorial concepts to gain insight into matrix problems spans many applications, from numerical analysis (sparse matrix theory) to dynamical systems (stability) to economics (sign solvability). Such analysis includes aspects of graph theory, since it is often useful to view a matrix as a combinatorial object, namely a graph or a directed graph. Problems involving sign (or zero-nonzero) pattern matrices occur in applications in, for example, economics, biology and chemistry, in systems where only the signs (or the zero-nonzero structure), rather than exact numeric values, for the entries in a connection matrix are known.