On the Convergence of Aluthge Sequence: a Review: Convergence of λ-Aluthge Sequence: Exploring the Properties of Nonzero Eigenvalues

Abstract

For 0 < λ < 1, the λ -Aluthge sequence {Δm λ (X)}m∈N converges if the nonzero eigenvalues of X ∈ Cn×n have distinct moduli, where Δλ (X) := P λUP1−λ if X= UP is a polar decomposition of X.