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 legislator should direct his attention above all to the education of youth; for the neglect of education does harm to the constitution. The citizen should be molded to suit the form of government under which he lives. For each government has a peculiar character which originally formed and which continues to preserve it. The character of democracy creates democracy, and the character of oligarchy creates oligarchy.”
—Aristotle (384–323 B.C.)