Kippenhahn's Theorem
 
 
Description:  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.

Date:  2018-11-28
Start Time:   15:00
Speaker:  Stephan Weis (CMUC, Univ. Coimbra)
Institution:  CMUC, Universidade de Coimbra
Place:  Room 5.5, DMat of University of Coimbra
Research Groups: -Algebra and Combinatorics
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