Hermitian form

Summary

A Hermitian form on a complex vector space is a sesquilinear form $h$ with $h(v, u) = \overline{h(u, v)}$ for all vectors $u, v$. It is the complex analogue of a symmetric bilinear form. The value $h(v, v)$ is always real, so Hermitian forms can be positive, negative or indefinite. Complex inner products are exactly the positive definite Hermitian forms.