English

Patterns that require distinct singular values

Combinatorics 2025-11-18 v1

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.

Keywords

Cite

@article{arxiv.2511.12641,
  title  = {Patterns that require distinct singular values},
  author = {Caleb Cheung and Bryan Shader},
  journal= {arXiv preprint arXiv:2511.12641},
  year   = {2025}
}
R2 v1 2026-07-01T07:39:50.544Z