The Inertia Set of Nonnegative Symmetric Sign Pattern with Zero Diagonal
Yubin Gao, Yanling Shao · Czechoslovak Mathematical Journal · 2003
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.