Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases

Steven Finch

Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases

Combinatorics 2026-07-08 v1 Discrete Mathematics Number Theory

Authors: Steven Finch

Abstract

How close to singularity can an $n \times n$ unimodular matrix be? For ternary cases as $n$ increases, exact expressions are unlikely, but upon fixing $n=4$ and assessing $(2k+1)$ -ary cases as $k$ increases, we make significant progress; similarly for $(k+1)$ -ary cases of $4\times 4$ nonnegative unimodular matrices.

Keywords

unimodular matrices matrix singularity ternary matrices nonnegative matrices combinatorial matrix theory

Cite

@article{arxiv.2607.07688,
  title  = {Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases},
  author = {Steven Finch},
  journal= {arXiv preprint arXiv:2607.07688},
  year   = {2026}
}

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20 pages