Skew symmetric

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

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