Essential sign change numbers of full signpattern matrices Article Swipe
Xiaofeng Chen
,
Wei Fang
,
Wei Gao
,
Yubin Gao
,
Guangming Jing
,
Zhongshan Li
,
Yanling Shao
,
Lihua Zhang
·
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.1515/spma-2016-0023
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.1515/spma-2016-0023
A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced for full sign patterns and condensed sign patterns. By inspecting the sign vectors realized by a list of real polynomials in one variable, a lower bound on the essential row and column sign change numbers is obtained. Using point-line confiurations on the plane, it is shown that even for full sign patterns with minimum rank 3, the essential row and column sign change numbers can differ greatly and can be much bigger than the minimum rank. Some open problems concerning square full sign patterns with large minimum ranks are discussed.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1515/spma-2016-0023
- https://www.degruyter.com/document/doi/10.1515/spma-2016-0023/pdf
- OA Status
- gold
- References
- 32
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2444456282
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https://openalex.org/W2444456282Canonical identifier for this work in OpenAlex
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https://doi.org/10.1515/spma-2016-0023Digital Object Identifier
- Title
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Essential sign change numbers of full signpattern matricesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2016Year of publication
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2016-06-16Full publication date if available
- Authors
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Xiaofeng Chen, Wei Fang, Wei Gao, Yubin Gao, Guangming Jing, Zhongshan Li, Yanling Shao, Lihua ZhangList of authors in order
- Landing page
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https://doi.org/10.1515/spma-2016-0023Publisher landing page
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https://www.degruyter.com/document/doi/10.1515/spma-2016-0023/pdfDirect link to full text PDF
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goldOpen access status per OpenAlex
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https://www.degruyter.com/document/doi/10.1515/spma-2016-0023/pdfDirect OA link when available
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Sign (mathematics), Mathematics, Combinatorics, Rank (graph theory), Matrix (chemical analysis), Point (geometry), Discrete mathematics, Geometry, Mathematical analysis, Materials science, Composite materialTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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