Abstract
Let A,B∈M n . The numerical range of a linear pencil Aλ−B is defined by W(Aλ−B)={t∈ C:tw *Aw−w *Bw=0 for some non-zero w∈ C n}. The numerical range of a linear pencil of n-by- n matrices coincides with the union of the numerical ranges of linear pencils of 2-by-2 matrices. We emphasize on computation of the numerical range of linear pencils of 2-by-2 matrices. Let A,B∈M 2 with constant diagonals. We show that the boundary of W(Aλ−B) lies on a rational curve of degree at most 4. By using Lagrange's multiplier and implicit function, we describe the boundary of W(Aλ−B) for general 2-by-2 matices.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
