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Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then the Aluthge transform is defined by

∆(T) = |T|1/2U|T|1/2.

Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), nN. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {∆n(T)}nN converges for every r × r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003.


This article was originally published in Revista de la Unión Matemática Argentina, available at

This work is distributed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).



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