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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© Centre for Mathematics, University of Coimbra, funded by
Science and Technology Foundation
Financiado total ou parcialmente pela FCT, Fundação para a Ciência e a Tecnologia, I.P., sob o Financiamento de:
UID/00324/2025 Projeto Estratégico com a referência DOI https://doi.org/10.54499/UID/00324/2025.
https://doi.org/10.54499/UID/PRR/00324/2025     UID/PRR/00324/2025   https://doi.org/10.54499/UID/PRR2/00324/2025   UID/PRR2/00324/2025
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