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arXiv · 1704.06745

A characterization of trace zero bisymmetric nonnegative $5 \times 5$ matrices

Somchai Somphotphisut·Keng Wiboonton
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Abstract

Let $λ_1 \geq λ_2 \geq λ_3 \geq λ_4 \geq λ_5 \geq -λ_1$ be real numbers such that $\sum_{i=1}^5 λ_i =0$. In \cite{oren}, O. Spector prove that a necessary and sufficient condition for $λ_1, λ_2, λ_3, λ_4, λ_5$ to be the eigenvalues of a symmetric nonnegative $5 \times 5$ matrix is "$λ_2+λ_5<0$ and $\sum_{i=1}^5 λ_{i}^{3} \geq 0"$. In this article, we show that this condition is also a necessary and sufficient condition for $λ_1, λ_2, λ_3, λ_4, λ_5$ to be the spectrum of a traceless bisymmetric nonnegative $5 \times 5$ matrix.

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Somchai Somphotphisut, Keng Wiboonton. 2017-04-28. A characterization of trace zero bisymmetric nonnegative $5 \times 5$ matrices. https://arxiv.org/abs/1704.06745

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