Random Matrices and Matrix Completion

TL;DR

This paper provides a self-contained proof of key results in low-rank matrix recovery, emphasizing the role of random matrix theory in identifying low-rank matrices from limited linear measurements.

Contribution

It offers a concise, accessible proof of main theorems in low-rank matrix recovery, integrating foundational aspects of random matrix theory.

Findings

Key results in low-rank matrix recovery are proven

Random matrix theory is essential for matrix completion

The notes serve as an educational resource

Abstract

The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited linear information exploiting in a crucial way their very special structure. As a crucial tool we develop also the basic statements of the theory of random matrices. The notes are based on a number of sources, which appeared in the last few years. As we give only the minimal amount of the subject needed for the application in mind, the reader is invited to study this further reading in detail.