## Abstract

Given an r × r complex matrix T , if T = U | T | is the polar decomposition of T , then, the Aluthge transform is defined by Δ ( T ) = | T | 1 / 2 U | T | 1 / 2 . Let Δ n ( T ) denote the n -times iterated Aluthge transform of T , i.e. Δ 0 ( T ) = T and Δ n ( T ) = Δ ( Δ n − 1 ( T ) ) , n ∈ N . We prove that the sequence { Δ n ( T ) } n ∈ N converges for every r × r diagonalizable matrix T . We show that the limit Δ ∞ ( ⋅ ) is a map of class C ∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r × r matrices with r different eigenvalues.

## Full Text

### Topics from this Paper

- Diagonalizable Matrix
- Map Of Class
- Complex Matrix
- Dense Set
- Open Set + Show 2 more

Create a personalized feed of these topics

Get Started#### Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call### Similar Papers

- Canadian Journal of Mathematics
- Jan 1, 1971

- Proceedings of the American Mathematical Society
- Feb 1, 1971

- Linear Algebra and its Applications
- Mar 1, 2001

- Multidimensional Systems and Signal Processing
- Jan 1, 2016

- arXiv: Statistical Mechanics
- Aug 25, 2014

- Random Operators and Stochastic Equations
- Jan 1, 2006

- Random Matrices: Theory and Applications
- Jul 12, 2019

- Linear and Multilinear Algebra
- Aug 1, 2012

- Linear and Multilinear Algebra
- Nov 1, 1986

- Proceedings of the American Mathematical Society
- Jan 1, 1972

- Glasgow Mathematical Journal
- Jul 1, 1983

- Linear and Multilinear Algebra
- Aug 1, 1995

- Journal of Circuits, Systems and Computers
- Oct 1, 2010

### Advances in Mathematics

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023

- Advances in Mathematics
- Dec 1, 2023