If $F$ is a finite dimensional vector spaces over $\mathbb R$, I have to show that suprimum norm with respect to two different bases are equivalent.
I know how to prove that in a finite dimentional vector space any two norms are equivalent. In that proof we use induction on dimention.
Edit: without using that (in finite dimentional spaces two norms are equivalent) How can one prove this.
I tried to do this but no result. Any help