A skew-Hermitian form (also called an antisymmetric sesquilinear form), is a sesquilinear form ε : V × V → C such that
Every skew-Hermitian form can be written as i times a Hermitian form.
If V is a finite-dimensional space, then relative to any basis {ei} of V, a skew-Hermitian form is represented by a skew-Hermitian matrix A:
The quadratic form associated to a skew-Hermitian form
- Q(z) = ε(z,z)
is always pure imaginary.
Read more about this topic: Sesquilinear Form
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