Definition:Antisymmetric Matrix

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Let $R$ be a ring.

Let $\mathbf A$ be a square matrix over $R$.

$\mathbf A$ is antisymmetric if and only if:

$\mathbf A = -\mathbf A^\intercal$

where $\mathbf A^\intercal$ is the transpose of $\mathbf A$.

Also known as

An antisymmetric matrix is also known as a skew-symmetric matrix.

Some sources hyphenate: anti-symmetric.

Also see

  • Results about antisymmetric matrices can be found here.