Supposing we have a symmetric matrix $A\in\Bbb \{\pm1,0\}^{n\times n}$ of rank $m<n$ with all $+1$ or all $-1$ or all $0$ as diagonals and no $0$ on non-diagonals, when do we have $A-I$ to be full rank?
2026-04-01 23:10:06.1775085006
If $A\in\Bbb \{\pm1,0\}^{n\times n}$ is symmetric of rank $<n$, does $A-I$ have rank $n$?
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