Small Matrices with Small Inverses: Unimodular Zerofree Cases
arXiv:2605.0369119.2
AI Analysis
Provides a theoretical classification of a rare balanced matrix property, relevant for linear algebra and combinatorial optimization.
The paper investigates unimodular matrices where both the matrix and its inverse have no zero entries and remain small, classifying such matrices up to symmetry.
We consider unimodular matrices $M$ such that neither $M$ nor $M^{-1}$ contain zero entries. Matrices typically exhibit a trade-off: small $M$ imply large $M^{-1}$. We investigate rare cases where both remain small, classify these matrices up to symmetry, and discuss aspects of this balanced setting.