Patterns that require distinct singular values

2025/11/16 by Cheung, Caleb, Shader, Bryan
#05C50 #15A18 #15A29 #15B57 #58C1 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.12641

Abstract

Patterns of m by n matrices of term-rank m for which every real matrix with the pattern has no multiple singular value are characterized. This generalizes Fiedler's characterization of the paths being the only graphs for which every real symmetric matrix with the given graph has no repeated eigenvalue.

Citations

• The Strong Singular Value Property for Matrices
• Sign Patterns of Orthogonal Matrices and the Strong Inner Product Property

Related

• Paths are generically realisable
• Two Distinct Eigenvalues from a New Graph Product
• On the minimum number of distinct eigenvalues of triangle-free strongly regular graphs
• The Graphs for which the Maximum Multiplicity of an Eigenvalue is Two
• Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph