Skew-symmetric matrix
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For matrices with antisymmetry over the complex number field, see Skew-Hermitian matrix.
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric[1]) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition[2]: p. 38
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In terms of the entries of the matrix, if denotes the entry in the -th row and -th column, then the skew-symmetric condition is equivalent to