Published October 15, 2021
| Accepted Version
Journal Article
Open
Minimal rank completions for overlapping blocks
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.Attached Files
Accepted Version - 2106.11267.pdf
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2106.11267.pdf
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Additional details
- Eprint ID
- 110309
- Resolver ID
- CaltechAUTHORS:20210818-204746474
- Created
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2021-08-18Created from EPrint's datestamp field
- Updated
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2021-08-18Created from EPrint's last_modified field