- #1

- 70

- 0

## Main Question or Discussion Point

Whilst trying to refresh myself on what a dual space of a vector space is I have confused myself slightly regarding conventions. (I am only bothered about finite dimensional vector spaces.)

I know what a vector space, a dual space and a basis of a vector space are but dual bases:

I seem to recall something about the delta function being used. Does every basis have a dual basis or just standard the bases (i.e. (1,0,..,0), (0,1,0,...,0) , ... (0, ... ,0,1) )? Does the delta function rule have to apply to a dual basis or is it just a condition which ensures that a dual basis of an orthonormal basis is also orthonormal?

I know what a vector space, a dual space and a basis of a vector space are but dual bases:

I seem to recall something about the delta function being used. Does every basis have a dual basis or just standard the bases (i.e. (1,0,..,0), (0,1,0,...,0) , ... (0, ... ,0,1) )? Does the delta function rule have to apply to a dual basis or is it just a condition which ensures that a dual basis of an orthonormal basis is also orthonormal?