2020/09/01 by Geryba, Titas, Spitkovsky, Ilya M.
#15A60 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2009.00272
A complete description of 4-by-4 matrices \beginbmatrixαI & C D & βI\endbmatrix, with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which C-D^* also is a scalar multiple of the identity. In particular cases when in addition α-β is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.