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arXiv · 1808.09484

Nonnegative Eigenvectors of Symmetric Matrices

Hunter Swan
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Abstract

For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different class of matrices, namely real symmetric matrices with exactly two eigenvalues. We also prove a partial converse, that among real symmetric matrices with any more than two eigenvalues there exist some having no nonnegative eigenvector.

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Hunter Swan. 2018-08-28. Nonnegative Eigenvectors of Symmetric Matrices. https://arxiv.org/abs/1808.09484

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