# The SHOCKING truth about determinants

I recently wrote an article about how to code rational arithmetic in Erlang. In the article, I mentioned that the criteria for two rationals `a/b` and `c/d` to be equal is if `ad - bc = 0`.

If you are even a little bit familiar with linear algebra, you will recognize that as a determinant.

So what’s the connection?

zx and I were talking about this in a chat, and ended up recording a short episode where I explained the connection.

zx understands the interpretation of the determinant as signed area. He is dimly aware of the interpretation of the determinant as describing whether or not a system of linear equations is invertible. Although I have never sat him down and explained the connection in full. I explained that connection quite clearly in my “Gaussian Elimination, Determinants, and Invertibility” playlist

I did previously explain some of the determinant ideas in episodes 9 and 10, particularly the link between determinants and quaternions. Links below.

My plan is to explain all of this linearly in the “Foundations of QAnal” series of blog posts and in the “Math for Programmers” playlist.

But if you want a bit of a peek ahead, or if you were wondering about the relationship, check out this video and/or some of the further references.