A note on real similarity to a diagonal dominant matrix

TL;DR

This paper explores conditions under which a real matrix, including Hurwitz matrices, can be similar to a diagonal dominant matrix, aiding in understanding matrix properties and stability.

Contribution

It introduces new conditions for real matrix similarity to diagonal dominant matrices, expanding theoretical understanding.

Findings

Provides criteria for similarity to diagonal dominant matrices.

Extends results to Hurwitz matrices and general real matrices.

Enhances matrix analysis techniques.

Abstract

This note presents several conditions to characterize real matrix similarity between a Hurwitz matrix (and then more generally, a real square matrix) and a diagonal dominant matrix.