On Some Bounds on the Perturbation of Invariant Subspaces of Normal Matrices with Application to a Graph Connection Problem

2021/03/17 by Subhrajit Bhattacharya, Bhattacharya, Subhrajit
Computer Science · Engineering · Mathematics · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2103.09413

openalex publication_date 2021/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide upper bounds on the perturbation of invariant subspaces of normal matrices measured using a metric on the space of vector subspaces of ℂⁿ in terms of the spectrum of both the unperturbed & perturbed matrices, as well as, spectrum of the unperturbed matrix only. The results presented give tighter bounds than the Davis-Khan sinΘ theorem. We apply the result to a graph perturbation problem.

Related

• Uniform bounds for invariant subspace perturbations
• Invariant subspace perturbation of a matrix with Jordan blocks
• Relative Perturbation Bounds for the Joint Spectrum of Commuting Tuple of Matrices
• A Perturbation Bound on the Subspace Estimator from Canonical Projections
• The Rotation of Eigenvectors by a Perturbation. III