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.


15A18 Eigenvalues, singular values, and eigenvectors
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