The simplified version of the Spielman and Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertiblity theorem

TL;DR

This paper presents a simplified version of the Spielman and Srivastava algorithm for proving the Bourgain-Tzafriri Restricted Invertibility Theorem, sacrificing optimal constants for greater simplicity.

Contribution

It offers a more accessible proof of the theorem by modifying the original argument, making it easier for the mathematics community to understand and apply.

Findings

Original argument still valid with simplified proof

Simplification involves sacrificing the best constants

Provides a more accessible proof for researchers

Abstract

By giving up the best constants, we will see that the original argument of Spielman and Srivastava for proving the Bourgain-Tzafriri Restricted Invertibility Theorem \cite{SS} still works - and is much simplier than the final version. We do not intend on publishing this since it is their argument with just a trivial modification, but we want to make it available to the mathematics community since several people have requested it already.