225 citations · 542 across the 32 of their papers we have counts for
Showing 2012Show all
2 papers · 1 filter
math.AG2012★ 29 cited
Hyperbolic polynomials, interlacers, and sums of squares
Mario Kummer, Daniel Plaumann, Cynthia Vinzant
Hyperbolic polynomials are real polynomials whose real hypersurfaces are nested ovaloids, the inner most of which is convex. These polynomials appear in many areas of mathematics,…
math.AG2012★ 62 cited
Determinantal representations of hyperbolic plane curves: An elementary approach
Daniel Plaumann, Cynthia Vinzant
If a real symmetric matrix of linear forms is positive definite at some point, then its determinant is a hyperbolic hypersurface. In 2007, Helton and Vinnikov proved a converse in…