Abstract
The inertia set of a symmetric sign pattern A is the set i(A) = {i(B) | B = B T ∈ 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.
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Gao, Y., Shao, Y. The Inertia Set of Nonnegative Symmetric Sign Pattern with Zero Diagonal. Czech Math J 53, 925–934 (2003). https://doi.org/10.1023/B:CMAJ.0000024531.10708.9f
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DOI: https://doi.org/10.1023/B:CMAJ.0000024531.10708.9f