Definition:Anti-Hermitian Matrix

Definition

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

$\mathbf A$ is anti-Hermitian if and only if:

$\mathbf A = -\mathbf A^\dagger$

where $\mathbf A^\dagger$ is the Hermitian conjugate of $\mathbf A$.

Also known as

An anti-Hermitian matrix is also called a skew-Hermitian matrix

Examples

Arbitrary Example

This is an example of an anti-Hermitian matrix:

$\begin {pmatrix} i & i \\ i & 0 \end {pmatrix}$

Also see

• Definition:Hermitian Matrix
• Definition:Hermitian Conjugate

• Results about anti-Hermitian matrices can be found here.

Source of Name

This entry was named for Charles Hermite.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): anti-Hermitian matrix
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hermitian conjugate
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): anti-Hermitian matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hermitian conjugate