How to prove that any two real finite dimensional vector spaces with the same dimension are isomorphic to one another?

Question

As the title says: Prove that any two real finite dimensional vector spaces with the same dimension are isomorphic to one another?

How would you approach this proof?

Actually, this may be a better dupe: https://math.stackexchange.com/questions/1025926/vector-spaces-of-the-same-finite-dimension-are-isomorphic?rq=1 There are likely other dupes, too. — Randall, Jul 30 '19 at 18:17

score 3 · Answer 1 · answered Jul 30 '19 at 18:14

3

Hint. Choose a basis for each. Since you know the dimension you know how many vectors there are in a basis,

answered Jul 30 '19 at 18:14

Ethan Bolker

1 Answers1