What Is a Skew-Symmetric Matrix?

A skew-symmetric matrix is a square matrix that is equal to the negative of its own transpose. Skew-symmetric matrices are also known as antisymmetric matrices.

Skew-symmetric matrices are easy to recognize visually. The diagonal elements of a skew-symmetric matrix are always zero. Each off-diagonal element is the negative of the corresponding element on the other side of the diagonal. For example, element A(12) of the matrix A is equal to -A(21), where A(12) is the element in the first row and the second column of the matrix. All skew-symmetric matrices are singular, which means that they have a determinant of zero and no inverse.