Symbols:Linear Algebra/Hermitian Conjugate

Hermitian Conjugate

$\mathbf A^\dagger$

Symbol used for the Hermitian conjugate of a matrix.

Let $\mathbf A = \sqbrk \alpha_{m n}$ be an $m \times n$ matrix over the complex numbers $\C$.

Then the Hermitian conjugate of $\mathbf A$ is defined and denoted:

$\mathbf A^\dagger = \sqbrk \beta_{n m}: \forall i \in \set {1, 2, \ldots, n}, j \in \set {1, 2, \ldots, m}: \beta_{i j} = \overline {\alpha_{j i} }$

where $\overline {\alpha_{j i} }$ denotes the complex conjugate of $\alpha_{j i}$.

That is, $\mathbf A^\dagger$ is the transpose of the complex conjugate of $\mathbf A$.

The $\LaTeX$ code for \(\mathbf A^\dagger\) is \mathbf A^\dagger .

Variant

$\mathbf A^*$

A variant symbol used for the Hermitian conjugate of a matrix.

The $\LaTeX$ code for \(\mathbf A^*\) is \mathbf A^* .

Sources

• 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): Hermitian conjugate