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Keywords:
eigenvalue; inertia; maximal inertia; rank-one perturbation; symmetric sign pattern
eigenvalue; inertia; maximal inertia; rank-one perturbation; symmetric sign pattern
Summary:
The inertia of an $n$ by $n$ symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order $n$. In this note we classify all the maximal inertias for symmetric sign patterns of order $n$, and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.
References:
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