Flat portions on the boundary of the Davis-Wielandt shell of 3-by-3 matrices (Q958011)

The Davis-Wielandt shell of an \(n \times n\) matrix \(T\) is defined as the set \[ W(T,T^*T)= \{(x^*Tx,x^*T^*Tx): x \in \mathbb C\times\mathbb R,\;x^*x=1\}. \] The main aim of the paper is to investigate the existence of flat portions on the boundary of the Davis-Wielandt shell for \(n=3\), or the joint numerical range in the case \(m=n=3\).