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What is a skew-symmetric matrix?

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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.

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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.

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