Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
403125 | Journal of Symbolic Computation | 2013 | 13 Pages |
Abstract
In 2007, Helton and Vinnikov proved that every hyperbolic plane curve has a definite real symmetric determinantal representation. By allowing for Hermitian matrices instead, we are able to give a new proof that relies only on the basic intersection theory of plane curves. We show that a matrix of linear forms is definite if and only if its co-maximal minors interlace its determinant and extend a classical construction of determinantal representations of Dixon from 1902. Like the Helton–Vinnikov theorem, this implies that every hyperbolic region in the plane is defined by a linear matrix inequality.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Daniel Plaumann, Cynthia Vinzant,