A matricial view of the Collatz conjecture

TL;DR

This paper links the Collatz conjecture to matrix nilpotency, suggesting a new algebraic perspective on understanding the problem's complexity.

Contribution

It introduces a novel matrix-based approach, connecting the Collatz conjecture to properties of adjacency matrices and their nilpotency.

Findings

Nilpotency of certain submatrices is equivalent to the aperiodic Collatz conjecture.

Provides an algebraic framework for analyzing the conjecture.

Suggests new avenues for mathematical investigation of the problem.

Abstract

In this note, it is shown that the nilpotency of submatrices of a certain class of adjacency matrices is equivalent to the aperiodic Collatz conjecture.