High Quality Content by WIKIPEDIA articles! We assume that the the underlying field is not of characteristic 2: that is, that 1 + 1 0 where 1 denotes the multiplicative identity and 0 the additive identity of the given field. Otherwise, a skew-symmetric matrix is just the same thing as a symmetric matrix. Sums and scalar multiples of skew-symmetric matrices are again skew-symmetric. Hence, the skew-symmetric matrices form a vector space. Its dimension is n(n–1)/2. Let Matn denote the space of n x n matrices. A skew-symmetric matrix is determined by n(n – 1)/2 scalars (the number of entries above the main diagonal); a symmetric matrix is determined by n(n + 1)/2 scalars (the number of entries on or above the main diagonal). If Skewn denotes the space of n x n skew-symmetric matrices and Symn denotes the space of n x n symmetric matrices and then since Matn = Skewn + Symn and Skewn Symn = {0}, i.e.

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