I need to find the inverse of a quadratic matrix $n \times n$ whose elements are all $1$s, except the antidiagonal elements which are all $-1$s. Is there any special approach that can be applied to this matrix?
2026-04-03 11:06:51.1775214411
Inverse matrix of a matrix of special structure
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Simple. Write it as a rank-one update to $-2J$, where $J$ is the reversal matrix. Then apply Sherman-Morrison formula.