On the Frobenius norm of the inverse of a non-negative matrix
We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly referred to as the S-matrix conjecture, for all dimensions larger than a small constant.
Authors
- Elsa Frankel
- John Urschel
Institutions
- Wellesley College (US)
- Massachusetts Institute of Technology (US)
Publication Details
- Journal
- Linear Algebra and its Applications
- Published
- 2024-12-06
- DOI
- https://doi.org/10.1016/j.laa.2024.11.030
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 0.00