Question about Lemma 1

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Very nice work!

I have a question about Lemma 1 in page 5. As stated, $Tr(H) = \sum_{\forall i} \lambda_{i} \ge \sigma(H)$, where $Tr(H)$ is the trace of the Hessian matrix, and $\sigma(H)$ represents its largest singular value. However, according to the introduction in Section 4, it seems that $\lambda$ refers to the eigenvalues of $H$. My linear algebra background is a bit weak, and I’m struggling to understand why this Hessian matrix's eigenvalues are always non-negative. Could you please provide some insights?