Definition:Hermitian Matrix

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

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

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

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

Also known as

A Hermitian matrix is also known just as a Hermitian.


Arbitrary Example

This is an example of a Hermitian matrix:

$\begin {pmatrix} 1 & i \\ -i & 1 \end {pmatrix}$

Also see

  • Results about Hermitian matrices can be found here.

Source of Name

This entry was named for Charles Hermite.

Historical Note

The Hermitian matrix was invented by Charles Hermite to solve certain problems in number theory.

However, it turned out to be crucial in the formulation by Werner Karl Heisenberg of his model of quantum mechanics.