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arXiv · 2212.11193

Maximal Generalized Rank in Graphical Matrix Spaces

Alexander Guterman·Roy Meshulam·Igor Spiridonov
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Abstract

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.

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Alexander Guterman, Roy Meshulam, Igor Spiridonov. 2022-12-21. Maximal Generalized Rank in Graphical Matrix Spaces. https://doi.org/10.1007/s11856-023-2508-6

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