I recently wrote an article about how to code rational arithmetic in Erlang. In the article, I mentioned that the criteria for two rationals
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.
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.