Continuous selections of the inverse numerical range map
Brian Lins, Parth Parihar · Linear and Multilinear Algebra · 2015
For a complex -by- matrix , the numerical range is the range of the map acting on the unit sphere in . We ask whether the multivalued inverse numerical range map has a continuous single-valued selection defined on all or part of . We show that for a large class of matrices, does have a continuous selection on . For other matrices, has a continuous selection defined everywhere on except in the vicinity of a finite number of exceptional points on the boundary of .