Sesquilinear Form - Skew-Hermitian Form

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

Famous quotes containing the word form:

    “The Republicans hardly need a party and the cumbersome cadre of low-level officials that form one; they have a bankroll as large as the Pentagon’s budget, dozens of fatted PACs, and the well-advertised support of the Christian deity.”
    —Barbara Ehrenreich (b. 1941)