Timothy Lochner

Today's beef with math: overloading the term "inverse". Inverse of a scalar: 1/n, aka n^-1 Inverse of a matrix: m^-1. So far so good. Inverse of vector: -v. What. Why not v^-1? Turns out both would be right. There is Additive and Multiplicative Inverses.

Of course we have the term "reciprocal" that also means Multiplicative Inverse. The bigger issue to me is when math libraries implement inverse(vector) as additive and inverse(matrix) as multiplicative. No consistency.

Moreover, vec*vec is element-wise, but mat*mat is not. But mat+mat *is* element-wise. Not infuriating at all. Hot take: At least for computer science, all basic math operators should be element-wise. Anything else should be a function. Dot, cross, transform, etc.

vec*vec element-wise literally shows up in math no-where though. In CS it's purely an acceleration technique for SSE/shaders for the most part. Also, multiplicative and additive inverses are not the same thing. In traditional vector-spaces there is no group action on vectors.

The entire point I’m making is that additive and multiplicative inverses are not the same, yet I see math libs with “inverse(mat)” be multiplicative while “inverse(vec)” is additive.

Right but then it's the math libs at fault right? Not the math itself?

I see you mention "math libs" later but your first tweet mentioned your "beef with math" so I was a bit confused