Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 545, Issue -, Pages 148-173Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2017.11.017
Keywords
Joint numerical range; Density matrices; Exposed face; Generic shape; Classification
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The joint numerical range W(F) of three hermitian 3-by-3 matrices F = (F-1, F-2, F-3) is a convex and compact subset in R-3. Generically we find that W(F) is a three-dimensional oval. Assuming dim(W(F)) = 3, every one- or two-dimensional face of W(F) is a segment or a filled ellipse. We prove that only ten configurations of these segments and ellipses are possible. We identify a triple F for each class and illustrate W(F) using random matrices and dual varieties. (C) 2018 Elsevier Inc. All rights reserved.
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