TITLE: How to prove the Hahn-Banach constructively
QUESTION [6 upvotes]: I am just wondering, how to prove the Hahn-Banach theorem constructively for a finite dimensional normed vector space.
Thanks in advance for any helpful answers.

REPLY [2 votes]: 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.