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Journal article
Sparks of symmetric matrices and their graphs
The Electronic journal of linear algebra, v 39, pp 591-606
21 Nov 2023
Abstract
The spark of a matrix is the smallest number of nonzero coordinates of any nonzero null vector. For real symmetric matrices, the sparsity of null vectors is shown to be associated with the structure of the graph obtained from the off-diagonal pattern of zero and nonzero entries. The smallest possible spark of a matrix corresponding to a graph is defined as the spark of the graph. Connections are established between graph spark and well-known concepts including minimum rank, forts, orthogonal representations, Parter and Fiedler vertices, and vertex connectivity.
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Details
- Title
- Sparks of symmetric matrices and their graphs
- Creators
- Louis Deaett - Quinnipiac UniversityShaun Fallat - University of ReginaVeronika Furst - Fort Lewis CollegeJohn Hutchens - University of San FranciscoLon Mitchell - Eastern Michigan UniversityYaqi Zhang - Drexel Univ, Dept Math, Philadelphia, PA USA
- Publication Details
- The Electronic journal of linear algebra, v 39, pp 591-606
- Publisher
- Int Linear Algebra Soc
- Number of pages
- 16
- Grant note
- American Institute of Mathematics (AIM)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001109962100001
- Scopus ID
- 2-s2.0-85178304747
- Other Identifier
- 991022117972604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics