Definition:Antisymmetric Matrix

Definition

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.

Sources

• 1980: A.J.M. Spencer: Continuum Mechanics ... (previous) ... (next): $2.1$: Matrices: $(2.3)$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): antisymmetric: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): antisymmetric matrix
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): symmetric matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): antisymmetric matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): symmetric matrix
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): antisymmetric matrix