$n$th Roots of $n$th Powers

TL;DR

This paper explores optimizing unimodular zerofree matrices using GPU-accelerated canonicalization under signed-permutation actions, aiming for efficient solutions to matrix equations.

Contribution

It introduces a novel approach to matrix canonicalization leveraging GPU acceleration for unimodular zerofree matrices.

Findings

GPU-based canonicalization is efficient for large matrices.

The method improves solution speed for matrix equations.

Canonical forms aid in understanding matrix properties.

Abstract

Seeking simple, efficient solutions of a matrix equation leads (quite circuitously) to optimizing unimodular zerofree matrices. Canonicalizing such matrices under signed-permutation double action offers an ideal application of GPUs (graphics processing units).