I am having a really hard time understanding what a dual basis is.
I understand that is the vector space of linear transformations from a vector space V onto its field of scalars F, also known as linear functionals.
I get this. What I am struggling on is how to find the dual basis and why it is defined the way it is.
We call the ordered basis of that satisfies , , the dual basis of
The book only gave on example using . I followed what they were doing but it doesn't help me understand the dual basis any better.
Based on the way we set up bases for any other vector space, I quess I figured that the dual basis would somehow be a set of linear functionals such that every linear functional could be written as a linear combination of these linear functionals.
I don't know, I am lost. Can someone explain this to me better or possibly refer me to a good website to read in more depth about dual spaces and dual bases?