Boundary generating curves of the \(c\)-numerical range
Let \(A\) be an \(n\)-by-\(n\) matrix and \(c=(c_1,\dots,c_n)\) be a real \(n\)-tuple. The \(c\)-numerical range of~\(A\) is the set \(W_c=\{\sum^n_{j=1}c_jx^*_jAx_j\mid \{x_1,\dots,x_n\}\) is an orthogonal basis of~\({\mathbb C}^n\}\). The authors obtain parametric representations of the boundary generating curve of the \(c\)-numerical range of a matrix and give a description of the boundary generating curves of the \(c\)-numerical range of certain types of nilpotent Toeplitz matrices. A sufficient condition for the boundary generating curve to be rational is obtained. Finally, the authors compute the boundary generating curves of the numerical ranges for several concrete matrices and classify the rationality of the curves.
scientific article; zbMATH DE number 1371392