Skew-symmetric matrix

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In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition In terms of the entries of the matrix, if a i j {\textstyle a_{ij}} denotes the entry in the i {\textstyle i} -th row and j {\textstyle j} -th column, then the skew-symmetric condition is equivalent to In characteristic not equal to 2, diagonal elements of a skew-symmetric matrix are zeros because each element must be its own negative.

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