Fantope (source code)
= Fantope
{title2=$\mathcal F_k=\{Y:0\preceq Y\preceq I,\ \operatorname{tr}Y=k\}$}
For an integer $0\leq k\leq n$, the fantope is the <convex hull> of rank-$k$ <orthogonal projection matrices> in $\mathbb R^n$. Equivalently, it consists of real <symmetric matrices> with <eigenvalues> in $[0,1]$ and <matrix trace> $k$. To prove the equivalence, apply the <spectral theorem for real symmetric matrices> and express the <eigenvalue> vector as a <convex combination> of the zero-one <extreme points> of the <capped simplex>. The <sum of the largest eigenvalues> is its <support function>.
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