Classification of Joint Numerical Ranges of Three Hermitian Matrices of Size Three
نویسنده
چکیده
The joint numerical range of three hermitian matrices of order three is a convex and compact subset W ⊂ R which is an image of the unit sphere S ⊂ C under the hermitian form defined by the three matrices. We label classes of the analyzed set W by pairs of numbers counting the exposed faces of dimension one and two. Generically, W belongs to the class of ovals. Assuming dim(W ) = 3, the faces of dimension two are ellipses and only ten classes exist. We identify an object in each class and use random matrices and dual varieties for illustrations.
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