Sesquilinear form

In the more general noncommutative setting, with right modules we take the second argument to be linear and with left modules we take the first argument to be linear.

A complex sesquilinear form can also be viewed as a complex bilinear map

The matrix representation of a complex Hermitian form is a Hermitian matrix.

The matrix representation of a complex skew-Hermitian form is a skew-Hermitian matrix.

That is, a sesquilinear form is reflexive precisely when the derived orthogonality relation is symmetric.

The specialization of the above section to skewfields was a consequence of the application to projective geometry, and not intrinsic to the nature of sesquilinear forms. Only the minor modifications needed to take into account the non-commutativity of multiplication are required to generalize the arbitrary field version of the definition to arbitrary rings.