On the Frobenius norm of the inverse of a non-negative matrix

2024/09/06 by Elsa Frankel, John Urschel, Frankel, Elsa +1
Computer Science · Mathematics · Engineering · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2409.04354

Abstract

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.

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