Elliptope
= Elliptope
{title2=$\mathcal E_N=\{X\succeq0:\operatorname{diag}X=\boldsymbol1\}$}
The set of real <positive semidefinite matrices> with unit diagonal. Equivalently, its members are <Gram matrices> of unit <vectors>, by the <real spectral theorem>. Every two-by-two <principal minor> gives $|X_{ij}|\leq1$, so the set is bounded; it is also closed, hence <compact> in finite <dimension>. This gives attainment of linear objectives used in <semidefinite programming>.