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{{distinguish|Alternant matrix}}
|content=<math>\begin{matrix}
\begin{bmatrix}
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{bmatrix}
\qquad
\begin{bmatrix}
1 & 0 & 0\\
0 & 0 & 1\\
0 & 1 & 0
\end{bmatrix}
\\
\begin{bmatrix}
0 & 1 & 0\\
1 & 0 & 0\\
0 & 0 & 1
\end{bmatrix}
\qquad
\begin{bmatrix}
0 & 1 & 0\\
1 & -1 & 1\\
0 & 1 & 0
\end{bmatrix}
\qquad
\begin{bmatrix}
0 & 1 & 0\\
0 & 0 & 1\\
1 & 0 & 0
\end{bmatrix}
\\
\begin{bmatrix}
0 & 0 & 1\\
1 & 0 & 0\\
0 & 1 & 0
\end{bmatrix}
\qquad
\begin{bmatrix}
0 & 0 & 1\\
0 & 1 & 0\\
1 & 0 & 0
\end{bmatrix}
\end{matrix}</math>}}
In [[mathematics]], an '''alternating sign matrix''' is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices generalize [[Permutation matrix|permutation matrices]] and arise naturally when using [[Dodgson condensation]] to compute a determinant. They are also closely related to the [[six-vertex model]] with ___domain wall boundary conditions from [[statistical mechanics]]. They were first defined by William Mills, [[David P. Robbins|David Robbins]], and Howard Rumsey in the former context.
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