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Gaussian Regularization of the Pseudospectrum and Davies' Conjecture
Jess Banks, Archit Kulkarni, Satyaki Mukherjee +1
A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every…
The Solution of the Kadison-Singer Problem
Adam W. Marcus, Nikhil Srivastava
These lecture notes are meant to accompany two lectures given at the CDM 2016 conference, about the Kadison-Singer Problem. They are meant to complement the survey by the same auth…
Interlacing Families III: Sharper Restricted Invertibility Estimates
Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in t…
Asymptotically Optimal Multi-Paving
Mohan Ravichandran, Nikhil Srivastava
Anderson's paving conjecture, now known to hold due to the resolution of the Kadison-Singer problem asserts that every zero diagonal Hermitian matrix admits non-trivial pavings wit…