Ladder Matrix Recovery from Permutations

TL;DR

This paper establishes conditions under which ladder matrices, a generalization of bounded rank matrices, can be uniquely recovered after entry permutations, using advanced algebraic methods.

Contribution

It introduces novel recovery guarantees for ladder matrices under permutations, expanding the scope beyond traditional low-rank matrix recovery.

Findings

Unique recovery guarantees for ladder matrices

Application of algebraic geometry methods

Generalization to broader matrix structures

Abstract

We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative algebra and algebraic geometry, for which we include a preparation as needed for a general audience.