Dual Spaces
Overview
The dual space of a vector space is the set of linear maps from the vector space to its field.
{% \omega : V \rightarrow \mathbb{R} %}
such that
{% \omega(a\vec{v}_1 + b\vec{v}_2) = a\omega(\vec{v}_1) + b\omega(\vec{v}_2) %}
The function {% \omega %} is referred to as a
one-form.
Dirac Notation
A vector in Dirac notation is represented as
{% | \psi > %}
A one-form is written as
{% < \psi | %}
{% < \psi | \psi > %}
