>>12817840>>12818245Only true for finite dimensional vector spaces.
Anyway, it's not really that amazing. A vector space isomorphism means the two objects are really the same, you are just representing their elements by different symbols.
The interesting subtlety is in the fact that even though V = V*, there is no canonical isomorphism which shows this. You need to make an (arbitrary) choice, some additional structure, to explicitly construct such an isomorphism. Notably, this is not so with showing V = V**. You need only the bare vector space axioms to construct that map.
