This paper finds that the bounded rank perturbations problem is equivalent to a completion problem for matrix pencils, suggesting new insights in linear algebra.
In this paper, we study a direct link between the bounded rank perturbations problem and the completion problem for matrix pencils. We conjecture that the bounded rank perturbations problem is, in fact, equivalent to a completion problem. We prove the conjecture in three cases: when the rank bound is one, when the involved pencils are of full row rank, and when the rank bound equals the rank distance of the involved matrix pencils.
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Dodig et al. (2025) studied this question.
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