I am just wondering, how to prove the HahnBanach theorem constructively for a finite dimensional normed vector space.
Thanks in advance for any helpful answers.
I am just wondering, how to prove the HahnBanach theorem constructively for a finite dimensional normed vector space. Thanks in advance for any helpful answers. 


Same way as for the infinite dimensional case, except you avoid Zorn's lemma by counting dimensions. 


The idea is to show that one can extend a linear functional from an $n$dimensional space to a space of dimension $n+1$ without increasing its norm. See, for instance, my notes (Lemma E.2) In fact, by doing so, you can prove THBT constructively for any separable space. 

