On Matrices with Elliptical Numerical Ranges
Ethan S. Brown, Ilya M. Spitkovsky · Linear and Multilinear Algebra · 2004
It is known that for several classes of matrices, including quadratic and certain tridiagonal matrices, the numerical range is an ellipse. We prove this result for a larger class of matrices, encompassing these published results as well as providing other sufficient conditions for ellipticity. The proof gives an explanation for this phenomenon and, in certain cases, provides an explicit description of the numerical range.