Document Type
Article
Department/Program
Mathematics
Journal Title
OPERATORS AND MATRICES
Pub Date
Fall 11-4-2016
Volume
10
Issue
4
Abstract
We extend the pre-image representation of exposed points of the numerical range of a matrix to all extreme points. With that we characterize extreme points which are multiply generated, having at least two linearly independent pre-images, as the extreme points which are Hausdorff limits of flat boundary portions on numerical ranges of a sequence converging to the given matrix. These studies address the inverse numerical range map and the maximum-entropy inference map which are continuous functions on the numerical range except possibly at certain multiply generated extreme points. This work also allows us to describe closures of subsets of 3-by-3 matrices having the same shape of the numerical range.
Recommended Citation
Spitkovsky, Ilya M. and Weis, Stephan, PRE-IMAGES OF EXTREME POINTS OF THE NUMERICAL RANGE, AND APPLICATIONS (2016). OPERATORS AND MATRICES, 10(4).
10.7153/oam-10-58
DOI
10.7153/oam-10-58
