Interlacing Families III: Sharper Restricted Invertibility Estimates

arXiv: Functional Analysis, 2017.

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Other Links: academic.microsoft.com|arxiv.org

Abstract:

We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafririu0027s Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm stable rank and that tighter bounds hold when the number of columns in the matr...More

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