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Published October 15, 2021 | Version Accepted Version
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Minimal rank completions for overlapping blocks

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Abstract

We consider the multi-objective optimization problem of choosing the bottom left block-entry of a block lower triangular matrix to minimize the ranks of all block sub-matrices. We provide a proof that there exists a simultaneous rank-minimizer by constructing the complete set of all minimizers.

Additional Information

© 2021 Elsevier Inc. Received 24 January 2021, Accepted 16 June 2021, Available online 21 June 2021. We thank the anonymous reviewer for suggesting a significantly shorter and more revealing proof of Theorem 1 than the one we originally discovered, from which the proof presented in this article has been adapted. The authors have no competing interests to declare.

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Eprint ID
110309
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CaltechAUTHORS:20210818-204746474

Related works

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https://arxiv.org/abs/2106.11267 (URL)

Dates

Created
2021-08-18
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Updated
2021-08-18
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