2 problems

Cosine covariance conjecture. For every $n\geq 1$, every correlation matrix $\Sigma$, and every $t\geq 0$,

Let $\lambda_n$ be the smallest nonnegative number such that … and let $\rho_n$ be the smallest nonnegative number such that … Here $\mathcal{B}_n^{sym}$ is the set of $n$ by $n$ s…