2 problems

Gau–Wang–Wu conjecture. If the numerical range $W(A)$ is a circular disc centered at the origin, then $A$ is rotationally invariant.

Let $T$ be a partial isometry on a $4$-dimensional complex Hilbert space, and suppose that $\operatorname{Rank} T=2$. A matrix $T$ is unitarily equivalent to a complex symmetric ma…