Let be the norm in the primal space , then the following expression defines dual norm:
The intuition for the finite-dimension space is how the linear function (element of the dual space) could stretch the elements of the primal space with respect to their size, i.e.
One can easily define the dual norm as:
- The dual norm is also a norm itself
- For any :
- if , where
- Let , then
- The Euclidian norm is self dual .