Localization of eigenvalues of Doubly Cyclic Matrices

Charles E. Baker, Boris S. Mityagin

Fix positive numbers $\alpha$ and $\beta$. For the family of doubly cyclic matrices of the form $diag(a_1,a_2,...,a_n)-diag(b_1,b_2,...,b_n){\Sigma }_{\ast }$, where ${\Sigma }_{\ast }$ is a permutation matri…