An eigenvalue inclusion set for matrices with a constant main diagonal entry (Q2337879)

Summary: A set to locate all eigenvalues for matrices with a constant main diagonal entry is given, and it is proved that this set is tighter than the well-known Geršgorin set, the Brauer set and the set proposed in [\textit{A. Melman}, Linear Multilinear Algebra 60, No. 2, 189--199 (2012; Zbl 1244.15012)]. Furthermore, by applying this result to Toeplitz matrices as a subclass of matrices with a constant main diagonal, we obtain a set including all eigenvalues of Toeplitz matrices.