Maximal Generalized Rank in Graphical Matrix Spaces

In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Guterman, Alexander, Meshulam, Roy, Spiridonov, Igor
Format: Article
Language:English
Subjects:
Combinatorial analysis
Graph theory
Subspaces
Online Access:Get full text
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Summary:In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.11193