What would be a reasonable sufficient condition on a real symmetric matrix that would force its eigenvector with largest eigenvalue (or one of its eigenvectors with maximal eigenvalue) to have only non-negative entries?
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asked Feb 13, 2022 at 21:35
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5$\begingroup$ en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem $\endgroup$– wladCommented Feb 13, 2022 at 21:40
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$\begingroup$ en.wikipedia.org/wiki/Metzler_matrix $\endgroup$– wladCommented Feb 13, 2022 at 21:48
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$\begingroup$ en.wikipedia.org/wiki/Z-matrix_(mathematics) $\endgroup$– wladCommented Feb 13, 2022 at 21:51
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3$\begingroup$ I think you're looking for this: sciencedirect.com/science/article/abs/pii/S0024379518301253 $\endgroup$– wladCommented Feb 13, 2022 at 22:10
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2$\begingroup$ Name of @wlad's reference: Tarazaga - On the structure of the set of symmetric matrices with the Perron–Frobenius property. Other links are Perron–Frobenius theorem, Metzler matrix, Z-matrix, and When can a matrix with negative entries have a completely non-negative dominant eigenvector?. $\endgroup$– LSpiceCommented Feb 13, 2022 at 23:05
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