Definition:Hermitian Operator

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Definition

Let $\HH$ be a Hilbert space.

Let $\mathbf T: \HH \to \HH$ be a bounded linear operator.


Then $\mathbf T$ is said to be Hermitian if and only if:

$\mathbf T = \mathbf T^*$

That is, if and only if it equals its adjoint $\mathbf T^*$.


Also known as

A Hermitian operator is also known as a self-adjoint operator.


Also see


Source of Name

This entry was named for Charles Hermite.


Sources