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In Quantum Mechanics, an operator is called unitary if its hermitian adjoint is equal to its inverse, ie. U+U = UU+ = 1.
Unitary operators can be used to describe symmetries of the space of quantum states; due to their property that they preserve the hermitian inner product: that is to say, if under some transfromation |A> goes to U|A> and |B> goes to U|B>, then <B| goes to <B|U+, and then
    <B|U+U|A> = <B|A>