Category:Definitions/Hermitian Conjugates

This category contains definitions related to Hermitian Conjugates.
Related results can be found in Category:Hermitian Conjugates.

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 $\mathbf A$.

Source of Name

This entry was named for Charles Hermite.