On a generalization of the Johnson-Newman theorem to multiple rank-one perturbations
Abstract
Wang and Zhao (Adv. Appl. Math. 173 (2026) 102994) generalized the classic Johnson-Newman theorem on simultaneous similarity of symmetric matrices from a single rank-one perturbation to multiple rank-one perturbations. However, their result applies only to specific rank-one perturbations, and the condition provided is computationally involved, relying on complex multivariate polynomials. We provide a simple proof of their result, leading to an improved version with a simplified condition that holds for arbitrary rank-one perturbations.
Fields of Study & Subjects
Matrix Theory and Algorithms
Advanced Optimization Algorithms Research
Stability and Control of Uncertain Systems
Publication details
- Journal / source
- Electronic Journal of Linear Algebra
- Publisher
- University of Wyoming Libraries
- Volume
- 42
- Pages
- 411–416
- Publication date
- 4 June 2026