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Linear Systems over Join-Blank Algebras

Jananthan, Hayden and Kim, Suna and Kepner, Jeremy (2017) Linear Systems over Join-Blank Algebras. In: 2017 IEEE MIT Undergraduate Research Technology Conference (URTC). IEEE , Piscataway, NJ, pp. 1-4. ISBN 978-1-5386-2535-4. http://resolver.caltech.edu/CaltechAUTHORS:20180220-074905461

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Abstract

A central problem of linear algebra is solving linear systems. Regarding linear systems as equations over general semirings (V, ⊕, ⊗, 0,1) instead of rings or fields makes traditional approaches impossible. Earlier work shows that the solution space X(A, w) of the linear system Av = w over the class of semirings called join-blank algebras is a union of closed intervals (in the product order) with a common terminal point. In the smaller class of max-blank algebras, the additional hypothesis that the solution spaces of the 1 × 1 systems A ⊗ v = w are closed intervals implies that X(A, w) is a finite union of closed intervals. We examine the general case, proving that without this additional hypothesis, we can still make X(A, w) into a finite union of quasi-intervals.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/URTC.2017.8284192DOIArticle
http://ieeexplore.ieee.org/document/8284192/PublisherArticle
https://arxiv.org/abs/1710.03381arXivDiscussion Paper
Additional Information:© 2017 IEEE.
Subject Keywords:linear algebra, matrices, lattices, linear systems
Record Number:CaltechAUTHORS:20180220-074905461
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180220-074905461
Official Citation:H. Jananthan, S. Kim and J. Kepner, "Linear systems over join-blank algebras," 2017 IEEE MIT Undergraduate Research Technology Conference (URTC), Cambridge, MA, USA, 2017, pp. 1-4. doi: 10.1109/URTC.2017.8284192
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84881
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:22 Feb 2018 03:37
Last Modified:22 Feb 2018 03:37

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