2000 Years of Matrix Multiplication
Several methods of solving linear equations of several unknowns are described in Hindu literature, dating from about 200CE onwards. In particular, Brahmagupta's method seems very similar to Gaussian elimination[1].
And then there are solutions to quadratics, cubics and biquadratics, pell's equations, etc.
1. https://archive.org/details/history-of-hindu-mathematics-2-b...
It’s interesting and cool to see how long it took, and how many people it took, for the abstraction of matrices and matrix algebra to develop (in addition to how well-traveled the road was before the people we’ve attributed to and named some of these techniques after). What this makes me wonder is: what abstractions might be in progress today but incomplete? Maybe it’s a fun thought experiment and there’s no way to know because the ideas haven’t occurred to anyone, or maybe some people already do have an idea but won’t ultimately be remembered for it when our progeny is able to explore it a little more deeply and explain it a little more clearly. Or, I don’t know, maybe the period of history where some things get forgotten is now over?
Pretty mind boggling that there were Babylonians solving simultaneous equations, and people knew Gaussian elimination in 3rd century BC China. I wonder if the simultaneous equations were actually used to guide any decisions made by Babylonian government
Determinants always fascinated me, partly (completely?) because of the cool sounding name. I always wanted to get intuition for them because their formula is so simple, which has always been deeply unsatisfying to me to just take on its face.
This article got me searching for a 3blue1brown video on determinants and now my mind is absolutely blown!
I have a stupid question. I still don't really fully understand why matrix multiplication came to be row by column. I mean you could define things as row by together with the transpose operator right? So why is row by column so obviously the right way to define multiplication?
They didn’t talk about matrix exponentiation, which appears all over system and control theory and quantum mechanics. I wrote them about this just now.