Antisymmetric matrix

An antisymmetric (or skew-symmetric) matrix is a matrix ${\displaystyle A}$ such that ${\displaystyle A^{T}=-A}$. In other words, a matrix is antisymmetric if it is equal to its negative transpose.

For example, the matrix

${\displaystyle A={\begin{bmatrix}0&1&2\\-1&0&-6\\-2&6&0\end{bmatrix}}}$

is anti-symmetric, because

${\displaystyle -A={\begin{bmatrix}0&-1&-2\\1&0&6\\2&-6&0\end{bmatrix}}=A^{T}}$.