Okay but somebody please explain to me the reason for prefix operator column-major notation. I digress… >> linear algebra doesn’t exist simply because humanit

Okay but somebody please explain to me the reason for prefix operator column-major notation. I digress… >> linear algebra doesn’t exist simply because humanity managed to concoct a system that coincidentally finds usage in many seemingly unrelated subjects I’m not a stranger to this field, but this article doesn’t make this case at all, and I’m not sure it can be made. Linear algebra is fundamentally a set of notation rules that people built upon and found ways to represent their problems with. It’s ubiquity in many fields is no more surprising than the observation that many different genre of literature are written in English, and somehow nobody is confused enough to think that flight instruction manuals are the domain of English rather than the range of it. There is no practical limit to the number of academic papers one can write which awkwardly contort a simple intuitive computation into an indecipherable representation in linear algebra. If you want the concept of linear algebra to consume all linearity that exists in the world, then fine, whatever, but then the notation sucks. You may call a continuous Fourier transform a linear operation, but try writing down the values of that matrix. No; there’s nothing fundamentally tying the inner-workings of the world to the mechanics of linear algebra, but has been considerable effort to adapt some narrowly-chosen set of mechanics to represent the world, and some subset of those things work out well, so that’s what we focus on. But this is just path dependency. A different set of rules for writing linear relationships could have worked out better, or worse, but it would have to get there regardless. I expect that the current system will disappear soon as the world shifts to talking about computational tensors, and more flexible rules about how to apply operations. Who says you can’t multiply a row by a row? That’s stupid; we can and should do better. Is the determinant magical, or is is just a an arbitrary series of shift-product-sum which is far more applicable in the general sense? Do we really need a whole matrix to describe a permutation? Linearity may be considered well-described when there is no longer any need for a separate course to teach the notation and tricks behind it. When I was in grad school, one of my favorite books was Gene Golub’s “Matrix Computations”. It really is an impressive book from an incredible mind, like a book on chess positions written by Bobby Fisher. Regardless, it was hard for me to go through it without wondering why such a thing exists. Much like chess, the human mind can become enamored with any simple set of rules that can be extended to sufficient complexity. Faced with a real problem, sometimes it helps me to get to a solution, and sometimes it distracts me from the solution. I can never be sure which is more common.