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The inertia set of nonnegative symmetric sign pattern with zero diagonal. (English) Zbl 1080.15501
Summary: The inertia set of a symmetric sign pattern $$A$$ is the set $$i(A)=\{i(B) \mid B=B^T \in Q(A)\}$$, where $$i(B)$$  denotes the inertia of real symmetric matrix  $$B$$, and $$Q(A)$$ denotes the sign pattern class of  $$A$$. In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern $$A$$ in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns  $$A$$ with zero diagonal that require unique inertia.

##### MSC:
 15A18 Eigenvalues, singular values, and eigenvectors
##### Keywords:
sign pattern; inertia; inertia set; unique inertia
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##### References:
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