Linear systems over join-blank algebras Article Swipe
Hayden Jananthan
,
Suna Kim
,
Jeremy Kepner
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1109/urtc.2017.8284192
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1109/urtc.2017.8284192
A central problem of linear algebra is solving linear systems. Regarding\nlinear systems as equations over general semirings (V,otimes,oplus,0,1) instead\nof rings or fields makes traditional approaches impossible. Earlier work shows\nthat the solution space X(A;w) of the linear system Av = w over the class of\nsemirings called join-blank algebras is a union of closed intervals (in the\nproduct order) with a common terminal point. In the smaller class of max-blank\nalgebras, the additional hypothesis that the solution spaces of the 1x1 systems\nAv = w are closed intervals implies that X(A;w) is a finite union of closed\nintervals. We examine the general case, proving that without this additional\nhypothesis, we can still make X(A;w) into a finite union of quasi-intervals.\n
Related Topics
Concepts
Join (topology)
Blank
Class (philosophy)
Mathematics
Product (mathematics)
Linear system
Point (geometry)
Space (punctuation)
Linear algebra
Pure mathematics
Algebra over a field
Discrete mathematics
Interval (graph theory)
Combinatorics
Computer science
Mathematical analysis
Geometry
Mechanical engineering
Engineering
Operating system
Artificial intelligence
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1109/urtc.2017.8284192
- OA Status
- green
- References
- 15
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W2763732214Canonical identifier for this work in OpenAlex
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https://doi.org/10.1109/urtc.2017.8284192Digital Object Identifier
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Linear systems over join-blank algebrasWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2017Year of publication
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2017-11-01Full publication date if available
- Authors
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Hayden Jananthan, Suna Kim, Jeremy KepnerList of authors in order
- Landing page
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https://doi.org/10.1109/urtc.2017.8284192Publisher landing page
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1710.03381Direct OA link when available
- Concepts
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Join (topology), Blank, Class (philosophy), Mathematics, Product (mathematics), Linear system, Point (geometry), Space (punctuation), Linear algebra, Pure mathematics, Algebra over a field, Discrete mathematics, Interval (graph theory), Combinatorics, Computer science, Mathematical analysis, Geometry, Mechanical engineering, Engineering, Operating system, Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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15Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.the | 29, 34, 41, 62, 67, 71, 75, 94 |
| abstract_inverted_index.into | 107 |
| abstract_inverted_index.make | 105 |
| abstract_inverted_index.over | 14, 40 |
| abstract_inverted_index.that | 70, 84, 98 |
| abstract_inverted_index.this | 100 |
| abstract_inverted_index.with | 56 |
| abstract_inverted_index.work | 27 |
| abstract_inverted_index.case, | 96 |
| abstract_inverted_index.class | 42, 64 |
| abstract_inverted_index.makes | 22 |
| abstract_inverted_index.rings | 19 |
| abstract_inverted_index.space | 31 |
| abstract_inverted_index.still | 104 |
| abstract_inverted_index.union | 49, 89, 110 |
| abstract_inverted_index.X(A;w) | 32, 85, 106 |
| abstract_inverted_index.called | 44 |
| abstract_inverted_index.closed | 51, 81 |
| abstract_inverted_index.common | 58 |
| abstract_inverted_index.fields | 21 |
| abstract_inverted_index.finite | 88, 109 |
| abstract_inverted_index.linear | 4, 8, 35 |
| abstract_inverted_index.order) | 55 |
| abstract_inverted_index.point. | 60 |
| abstract_inverted_index.spaces | 73 |
| abstract_inverted_index.system | 36 |
| abstract_inverted_index.Earlier | 26 |
| abstract_inverted_index.algebra | 5 |
| abstract_inverted_index.central | 1 |
| abstract_inverted_index.examine | 93 |
| abstract_inverted_index.general | 15, 95 |
| abstract_inverted_index.implies | 83 |
| abstract_inverted_index.problem | 2 |
| abstract_inverted_index.proving | 97 |
| abstract_inverted_index.smaller | 63 |
| abstract_inverted_index.solving | 7 |
| abstract_inverted_index.systems | 11 |
| abstract_inverted_index.without | 99 |
| abstract_inverted_index.algebras | 46 |
| abstract_inverted_index.solution | 30, 72 |
| abstract_inverted_index.systems. | 9 |
| abstract_inverted_index.terminal | 59 |
| abstract_inverted_index.equations | 13 |
| abstract_inverted_index.intervals | 52, 82 |
| abstract_inverted_index.semirings | 16 |
| abstract_inverted_index.additional | 68 |
| abstract_inverted_index.approaches | 24 |
| abstract_inverted_index.hypothesis | 69 |
| abstract_inverted_index.join-blank | 45 |
| abstract_inverted_index.impossible. | 25 |
| abstract_inverted_index.instead\nof | 18 |
| abstract_inverted_index.shows\nthat | 28 |
| abstract_inverted_index.systems\nAv | 77 |
| abstract_inverted_index.traditional | 23 |
| abstract_inverted_index.the\nproduct | 54 |
| abstract_inverted_index.of\nsemirings | 43 |
| abstract_inverted_index.Regarding\nlinear | 10 |
| abstract_inverted_index.closed\nintervals. | 91 |
| abstract_inverted_index.quasi-intervals.\n | 112 |
| abstract_inverted_index.(V,otimes,oplus,0,1) | 17 |
| abstract_inverted_index.max-blank\nalgebras, | 66 |
| abstract_inverted_index.additional\nhypothesis, | 101 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.17122218 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |