On the boundary of weighted numerical ranges
arXiv:1403.3479 · doi:10.1080/03081087.2015.1043117
Abstract
In this article, we are going to introduce the weighted numerical range which is a further generalization both the c-numerical range and the rank k numerical range. If the boundaries of weighted numerical ranges of two matrices (possibly of different sizes) overlap at sufficiently many points, then the two matrices share common generalized eigenvalues.