Definition:Anti-Hermitian Matrix
(Redirected from Definition:Skew-Hermitian Matrix)
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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
- 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