A Necessary Condition for the Spectrum of Nonnegative Symmetric $5\times 5$ Matrices

Raphael Loewy, Oren Spector

Let $A$ be a nonnegative symmetric $5\times 5$ matrix with eigenvalues ${\lambda }_1\ge {\lambda }_2\ge {\lambda }_3\ge {\lambda }_4\ge {\lambda }_5$. We show that if ${\sum }_{i=1}^5{\lambda }_i\ge \frac{1}{2}{\lambda }_1$…