The \(q\)-numerical range of a reducible matrix via a normal operator (Q865407)

It is shown that the \(q\)-numerical range of a reducible \(3\times 3\) matrix is determined by the \(q\)-numerical range of the normal operator \((Tf)(z) =zf(z)\), \(f\in L^2(\Delta,dx,dy)\) for some compact convex set~\(\Delta\). This result provides a performable algorithm to compute the boundary of the \(q\)-numerical range of a reducible \(3\times 3\) matrix. An example is given to illustrate computations.