= Basis of the space of real skew-symmetric matrices
{title2=$\{E_{ij}-E_{ji}:i<j\},\quad\dim=n(n-1)/2$}
For real $n\times n$ <skew-symmetric matrices>, each upper-triangular entry can be chosen freely, the corresponding lower-triangular entry is its negative, and diagonal entries vanish. Thus the displayed <matrix unit> differences span the space and are <linearly independent>: inspecting entry $(i,j)$ with $i<j$ recovers its coefficient. There are $n(n-1)/2$ such pairs, giving the <dimension>.
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