Definition:Self-Adjoint Operator

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Let $H$ be a Hilbert space.

Let $A \in B \left({H}\right)$ be a bounded linear operator.

Then $A$ is said to be self-adjoint or hermitian iff:

$A = A^*$

That is, if it equals its adjoint $A^*$.

Source of Name

This entry was named for Charles Hermite.

Also see