Combined perturbation bounds for eigenstructure of Hermitian matrices and singular structure of general matrices

2025/09/12 by Chen, Xiao Shan, Xu, Hongguo
#65F15 #65F99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2509.10688

Abstract

Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary calculus techniques.

Citations

• First-order Perturbation Theory for Eigenvalues and Eigenvectors
• The Rotation of Eigenvectors by a Perturbation. III

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• Quadratic perturbation bounds for generalized eigenvalue problems
• The extension of Weyl-type relative perturbation bounds
• A Note on Eigenvalues of Perturbed Hermitian Matrices
• Relative Perturbation Bounds for the Joint Spectrum of Commuting Tuple of Matrices