All Questions

Consider the Stiefel manifold $$\mathrm{St}(n,k) :=\{X \in \mathbb{R}^{n\times k} : X^TX = I_k\},$$ where $I_k$ is the $k$-dimensional identity matrix. It is well known that $$\mathrm{conv} \left( ...

Suppose I have a convex set $C\subset\mathbb{R}^n$ such that $0\in C$ and every Cauchy sequence in $C$ converges in $C$, but $C$ need not be bounded. (Actually I want unbounded $C$). Consider the set ...