Ovals of Cassini for Toeplitz matrices
A. Melman · Linear and Multilinear Algebra · 2011
Both the Gershgorin and Brauer eigenvalue inclusion sets reduce to a single disc when applied to a matrix with a constant main diagonal. We show that a union of ovals of Cassini containing all the eigenvalues of such a matrix can nonetheless be derived and that this union is guaranteed to lie inside the Brauer set. We then apply our results to Toeplitz matrices.