|
The numerical range of a matrix is a convex subset of the plane of complex numbers (Toeplitz 1919, Hausdorff 1919) and equals the convex hull of a real algebraic curve (Kippenhahn 1951, Chien and Nakazato 2010). An interesting higher-dimensional analogue would be to write the joint algebraic numerical range of three or more hermitian matrices in terms of the convex hull of a real variety. In this talk, we explain a convex hull representation for the dual cone of a hyperbolicity cone (Sinn, 2015). We translate Sinn's result into the desired convex hull representation of the joint algebraic numerical range, and we discuss examples.
|
