Maximal rank in matrix spaces via graph matchings

2017/03/16 by Roy Meshulam, Meshulam, Roy
Computer Science · Mathematics · #05C50 (Primary) #47L05 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1703.05551

openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in terms of their maximal rank.

Related

• A note on spaces of symmetric matrices
• Affine spaces of symmetric or alternating matrices with bounded rank
• The rank distribution of matrices representing graphs with a long induced path over the field of two elements
• On affine spaces of alternating matrices with constant rank
• Connections between graphs and matrix spaces