Speaker
Kennett Dela Rosa
(University of the Philippines Diliman)
Description
This study considers some problems involving the $k$-numerical range. Following the idea of the zero-dilation index, the notion of the zero-trace index is introduced, which is defined as the largest zero-trace compression of a matrix. Alternative characterization of the zero-trace index is given, and zero-trace indices of certain classes of matrices are identified. The study also considers recent results on the numerical range of cyclic shift matrices. A recent solution to a conjecture proved that a certain arrangement of the weights of a given cyclic shift matrix maximizes the classical numerical range. This work explores whether analogous optimal arrangements exist for the $k$-numerical range.
Author
Kennett Dela Rosa
(University of the Philippines Diliman)