# Real and complex integral closure, Lipschitz equisingularity and applications on square matrices

## TL;DR

This paper advances the understanding of Lipschitz triviality and integral closure for matrix singularities, applying these concepts to classify and analyze square matrix singularities.

## Contribution

It extends integral closure results to the real setting and improves previous findings on Lipschitz triviality of matrix germs.

## Key findings

- Extended integral closure results for real matrices
- Improved criteria for Lipschitz triviality of matrix germs
- Application to classification of square matrix singularities

## Abstract

Recently the authors investigated the Lipschitz triviality of simple germs of matrices. In this work, we improve some previous results and we present an extension of an integral closure result for the real setting. These tools are applied to investigate classes of square matrices singularities classified by Bruce and Tari.