[[File:Alternating Sign Matrices of Size 3.svg|400px|thumb|right|The seven alternating sign matrices of size 3.]]
In [[mathematics]], an '''alternating sign matrix''' is a square matrix of 0's0s, 1's1s, and −1's1s 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.
