An independent proof of the even-dimensional S-matrix inequality

Yinjie Li

Harwit and Sloane conjectured that every nonsingular entrywise-nonnegative matrix $A\in {\mathbb{R}}^{n\times n}$ satisfies $\Vert A^{-1}{\Vert }_F\ge 2n(n+1{)}^{-1}\Vert A{\Vert }_{\max }^{-1}$, with equali…