Slides
** Title: ** Quantitative Diagonalizability

##### **Speaker: ** Nikhil Srivastava (UC Berkeley, USA)

##### **Date: **16 August 2019

**Time:** 3 – 5 pm (with a 15 minute break at 3:45)

#####
**Venue: ** LH-1, Mathematics Department

A diagonalizable matrix has linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every matrix is the limit of diagonalizable matrices. We prove a quantitative version of this fact: every n x n complex matrix is within distance delta of a matrix whose eigenvectors have condition number poly(n)/delta, confirming a conjecture of E. B. Davies. The proof is based on regularizing the pseudospectrum with a complex Gaussian perturbation.

Joint work with J. Banks, A. Kulkarni, S. Mukherjee.

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Last updated: 03 Feb 2023