Dirac notation

Note a different choice of conventions used in math and physics communities:

\[( a, b ) = \braket{b}{a} = \sum_i^N b_i^* a_i\]

and

\[\bra{\psi}A\ket{\psi} = \braket{\psi}{A\psi} = (A\psi, \psi) \neq (\psi, A\psi).\]

Note that

\[\braket{b}{a} \in \mathbb{C}.\]