Corpus ID: 195699896

Gaussian Regularization of the Pseudospectrum and Davies' Conjecture

@article{Banks2019GaussianRO,
  title={Gaussian Regularization of the Pseudospectrum and Davies' Conjecture},
  author={Jessica E. Banks and Archit Kulkarni and S. Mukherjee and N. Srivastava},
  journal={ArXiv},
  year={2019},
  volume={abs/1906.11819}
}
A matrix $A\in\mathbb{C}^{n\times n}$ is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every $A\in \mathbb{C}^{n\times n}$ is the limit of diagonalizable matrices. We prove a quantitative version of this fact conjectured by E.B. Davies: for each $\delta\in (0,1)$, every matrix $A\in \mathbb{C}^{n\times n}$ is at least $\delta\|A\|$-close to one whose eigenvectors have condition number at worst $c_n/\delta… Expand
6 Citations

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