Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110052We prove that for any $n\times n$ matrix, $A$, and $z$ with $|z|\geq \|A\|$, we have that $\|(z-A)^{-1}\|\leq\cot (\fracπ{4n}) \dist (z, \spec(A))^{-1}$. We apply this result to the study of random orthogonal polynomials on the unit circle.27 pagesSpectral TheoryClassical Analysis and ODEs34L15, 05E35, 47B35Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circletext