TY - ELEC
AU - Rainer Sinn
PY - 2019
TI - KippenhahnÃ¢s Theorem for the joint numerical range
LA - eng
M3 - Moving Image
AB - By the Toeplitz-Hausdorff theorem in convex analysis, the numerical range of a complex square matrix is a convex compact subset of the complex plane. Kippenhahn's theorem describes the numerical range as the convex hull of an algebraic curve that is dual to a hyperbolic curve. For the joint numerical range of several matrices, the direct analogue of Kippenhahn's theorem is known to fail. We discuss the geometry behind these results and prove a generalization of Kippenhahn's theorem that holds in any dimension. Joint work with Daniel Plaumann and Stephan Weis.
N2 - By the Toeplitz-Hausdorff theorem in convex analysis, the numerical range of a complex square matrix is a convex compact subset of the complex plane. Kippenhahn's theorem describes the numerical range as the convex hull of an algebraic curve that is dual to a hyperbolic curve. For the joint numerical range of several matrices, the direct analogue of Kippenhahn's theorem is known to fail. We discuss the geometry behind these results and prove a generalization of Kippenhahn's theorem that holds in any dimension. Joint work with Daniel Plaumann and Stephan Weis.
UR - https://open.library.ubc.ca/collections/48630/items/1.0385852
ER - End of Reference