Element-wise Convergence Behavior of Subspace Iteration

This paper studies the element-wise convergence behavior of subspace iteration. All results are established for both \(\mathbb{F}=\mathbb{R}\) and \(\mathbb{F}=\mathbb{C}\). For a diagonal matrix \(Λ=\mathrm{diag}(λ_1,\ldots,λ_n)\) with \(|λ_1|>\cdots>|λ_n|>0\), we analyze the modulus of each entry