Non-normal matrices are ubiquitous in various branches of science, such as fluid dynamics, mathematical physics, partial differential equations, and many more. Non-normality causes notorious sensitivity of the eigenvalues, and the eigenvalue analysis often turns out to be misleading. These motivate the study of pseudospectrum, and the spectral properties of random perturbation of non-normal matrices. In the first part of the talk, we will introduce these issues and their resolutions through some fun experiments and simulations. In the latter half, we will move to describe spectral properties of random perturbations of non-normal Toeplitz matrices, where over the last few years a coherent theory has emerged.

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Last updated: 28 Nov 2023