Authors: Dodig, Marija 
Stošić, Marko 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Bounded rank perturbations of matrix pencils without nontrivial invariant factors
Journal: Linear and Multilinear Algebra
Issue Date: 2023
Rank: ~M22
ISSN: 0308-1087
DOI: 10.1080/03081087.2023.2277210
In this paper, we solve the bounded rank perturbation problem for matrix pencils without nontrivial homogeneous invariant factors, over arbitrary fields. The solution is based on reducing the problem to two minimal case matrix pencil completion problems. If there are no nontrivial homogeneous invariant factors involved, these two minimal completion problems allow treating column and row minimal indices separately. This is an example of the utility of completion tools in perturbation problems, when dealing with matrix pencils.
Keywords: Low rank perturbations | matrix pencils | minimal completions
Publisher: Taylor & Francis

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