Theorem 4.29 (Marcus, Spielman, Srivastava (matrix)). Assuming that:

$r_{1}, \dots, r_{m} \in ℝ^{n}$ are independent random vectors, whose support has $\leq 2$ points

Then

𝔼 \det (x I - \sum_{j = 1}^{m} r_{j} r_{j}^{⊤})

is real rooted.