How well-conditioned can the eigenvector problem be?
Carlos Beltrán, Laurent Bétermin, Peter J. Grabner, Stefan Steinerberger · Mathematics of Computation · 2021
The condition number for eigenvector computations is a well-studied quantity. But how small can it possibly be? Specifically, what matrices are perfectly conditioned with respect to eigenvector computations? In this note we answer this question for n × n n \times n matrices, giving a solution that is exact to first-order as n → ∞ n \rightarrow \infty .