Category:Definitions/Hermitian Conjugates
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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.
Pages in category "Definitions/Hermitian Conjugates"
The following 7 pages are in this category, out of 7 total.