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

我的研究主要涉及组合矩阵分析，其中组合方法用于解决和更好地理解矩阵理论问题。使用组合概念来洞察矩阵问题跨越了许多应用，从数值分析（稀疏矩阵理论）到动力系统（稳定性）到经济学（符号可解性）。这种分析包括图论的各个方面，因为将矩阵视为组合对象（即图或有向图）通常是有用的。涉及符号（或零-非零）模式矩阵的问题出现在诸如经济学、生物学和化学等领域的应用中，在这些系统中，连接矩阵中的条目只知道符号（或零-非零结构），而不知道精确的数值。

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.