Abstract
The principal concern of this paper is with real matrices whose undirected graphs are trees. To better understand potential stability of sign pattern classes, two simple criteria are given that preclude stability throughout a sign pattern class. In addition, those sign patterns that preclude eigenvalues with real part equal to 0 are characterized and the constant inertia within such classes is determined. Such tests may be computationally significant, as calculations with specific matrices may be subject to round off error uncertainties.
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