Definition
Sesquilinearity
A map
on a vector space over a field is sesquilinear if it is linear in one argument and semilinear in the other. The two assignments are equivalent via conjugate symmetry. Mathematical Convention
The mathematical convention makes the first argument linear, i.e. for all
and : Bra-Ket (Physics) Convention
In bra-ket notation (and in physics) the opposite convention is used: the ket (second argument) is the linear side, the bra is the semilinear side: