A family of matrix flows converging to normal matrices
Functional Analysis
2026-02-13 v1 Dynamical Systems
Operator Algebras
Spectral Theory
Abstract
The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. We introduce a family of matrix flows that share this convergence property by defining them through ordinary differential equations. The family includes a continuous analogue of the Aluthge transform, as well as a differential equation discussed by Haagerup in the context of II factors. We also examine the same type of flows in the setting of Hilbert space operators equipped with unitarily invariant norms.
Keywords
Cite
@article{arxiv.2602.11837,
title = {A family of matrix flows converging to normal matrices},
author = {Masaki Izumi},
journal= {arXiv preprint arXiv:2602.11837},
year = {2026}
}