New pairs of matrices with convex generalized numerical ranges

Wai-Shun Cheung

In this article, we are going to search for $n\times n$ matrices $A$ and $B$ such that their generalized numerical range $$W_A(B)=\{tr(A{U}^{\ast }BU):U^{\ast }U=U{U}^{\ast }=I\}$$ is convex. More…