In

Quantum Mechanics, the hermitian adjoint of an operator A is denoted A

^{+}, and is defined to be

*the* operator that satisfies

<x|A|y> = <y|A^{+}|x>^{*}

for all states labeled by x and y. By taking these labels to be discrete, the matrix A

_{ij} =

<i|A|j

> can be said to be hermitian if its

transpose is equal to its

complex conjugate.

Hermitian operators are said to correspond to observables (that is, their eigenvalues are the quantities that are measured by experiment), which is awfully handy since their eigenvalues are all real.