Numerical range of real-valued linear mapping on the complex Stiefel manifold: Convexity and application

Abstract

The study confirms the convexity of the joint numerical range of any k real-valued linear functions on the $n\times p$ complex Stiefel manifold under the condition $k\le 2n-2p+1$. Revealing the hidden convexity of fractional linear programming on the complex Stiefel manifold, a first-time study, serves as an impactful application.