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Showing 2006 · math.SPShow all
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math.SP2006★ 1 cited
Perturbations of Jordan Matrices
E B Davies, Mildred Hager
We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are…
math.SP2006★ 1 cited
Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle
E. B. Davies, Barry Simon
We prove that for any matrix, , and with , we have that $\|(z-A)^{-1}\|\leq\cot (\fracπ{4n}) \dist (z, \spec(A))^{-1}$. We apply this result to th…