Sign Pattern Matrices
The study of sign pattern matrices is an important part of combinatorial matrix theory. It has a rich theory in its own right and, in addition, some results are useful in applications to dynamical systems where sign patterns arise naturally, for example in predator-prey populations, economics, chemistry, and sociology. The aim of this chapter is to describe some spectral properties of matrices with a given sign pattern from the perspective of combinatorial matrix theory, showing some results, techniques, applications, and open problems. Topics are chosen from the literature on sign patterns; some of these and other related topics can be found in the book Brualdi–Shader , and in the chapter Hall–Li  from the Handbook of Linear Algebra edited by L. Hogben, and references therein. Readers are encouraged to consult these other references for topics beyond those in this chapter, which is a somewhat personal overview of some results on sign pattern matrices.
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