On Matrices with Perron–Frobenius Properties and Some Negative Entries

By Charles R. Johnson, P. Tarazaga. 2004

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Eventually positive semigroups of linear operators (2015, background): “As noted in the introduction, a sophisticated finite-dimensional theory of eventually positive operators and semigroups has been developed during the last twenty years; see for instance [21, 25] for results about eventually positive matrices and [26] for eventually positive matrix semigroups.”
Eventually and asymptotically positive semigroups on Banach lattices (2015, background): “eration of inverse eigenvalues problems (see e.g. [11, 26, 54] or[48, p48–54])andby an attempt togeneralise the classical Perron–Frobenius type spectral results to a wider class of matrices (see e.g. [21, 36]). An analysis of continuous-time eventually positive matrix semigroups can for example be f”
ON GENERAL MATRICES HAVING THE PERRON-FROBENIUS PROPERTY ∗ (2008, methodology): “The set PF2 is characterized as the set of all 2× 2 matrices with positive offdiagonal entries and positive trace [16].”