Convergence of iterated Aluthge transform sequence for diagonalizable matrices

J. Antezana, E. Pujals, D. Stojanoff

Given an $r\times r$ complex matrix $T$, if $T=U|T|$ is the polar decomposition of $T$, then, the Aluthge transform is defined by $$\Delta (T)=|T{|}^{1/2}U|T{|}^{1/2}.$$ Let ${\Delta }^n(T)$…