The recent topics I studied were linear functionals and dual spaces. I like to think about a linear functional as a stack of hyperplanes like it is described here.
In "Finite dimensional vector spaces" by Paul Halmos I read that every vector space is isomorphic to its double dual. I wonder if there is an intuitive way to see that they are isomorphic? Also I am not sure how I could graphically or geometrically think about the double dual space (in the sense I think about the dual space as a stack of hyperplanes in every direction). Is there a way to visualize the double dual space? Maybe then the isomorphism would become clearer. I guess there is some intuition behind it since someone had to think about it first before he or she invented the concept (double dual space). I hope my question makes sense?
Thanks for any responses!