Abstract
An n-by-n () weighted shift matrix A is one of the form where the ’s, called the weights of A, are complex numbers. Let denote the -by- principal submatrix of A obtained by deleting its jth row and jth column. We show that the boundary of numerical range W(A) has a line segment if and only if the ’s are nonzero and for some . This refines previous results of Tsai and Wu on numerical ranges of weighted shift matrices. In addition, we give an example showing that there is a weighted shift matrix with line segments on the boundary of its numerical range such that the moduli of its weights are not periodic.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.