4 problems

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

The open elliptope of full-rank correlation matrices carries quotient-Lie-Cholesky metrics obtained from the congruence action of matrix Lie groups, generalizing quotient-affine me…

Let $d$ be a positive integer, and let $\mathcal P_d^{\text{U}}$ and $\mathcal P_d$ denote the classes of correlation matrices attainable, respectively, by $d$-dimensional random v…

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…