Linear Systems over Join-Blank Algebras
- Creators
- Jananthan, Hayden
- Kim, Suna
- Kepner, Jeremy
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.
Additional Information
© 2017 IEEE.Attached Files
Submitted - 1710.03381.pdf
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Additional details
- Eprint ID
- 84881
- Resolver ID
- CaltechAUTHORS:20180220-074905461
- Created
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2018-02-22Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field