Taking Vector Transposes Seriously | Jiahao Chen | JuliaCon 2017

If you want a great video on the topic, see ▶ this video Or equivalently link There are basically two self-consistent choices for the design of linear algebra libraries.

If you will do a lot of matrix stuff you might want to listen to ▶ this video taking Vector Transpose Seriously

> Purist test The short answer is. Yes, but if your PL treats it that way you will wind up in trouble [0]. The long answer is: ▶ this video (but seriously take the time to watch this, it's fantastic). [0] Separately C- and often C-derived languages/frameworks like numpy also treat them as 1xN matrices, but that's a nearly tabs-vs-spaces level religious war, with actual consequences. I think a lot of people got confused when translating andrew ng's early octave-based ML coursera course (Nx1) to python (1xN), and also in the back and forth between math ML papers which use Nx1 and python.

I happened to be the other way, I learned first that matrices were linear transformations and, being thick-headed, it took me a really long time to understand that matrices could also be used as "dumb excel spreadsheets". there's a fantastic historiography of linear algebra and why we're stuck in this situation here: ▶ this video

Addendum: Also really good is this video about how one should treat vectors and matrices in a type system. Has good lessons for python, R, and Matlab. Seriously anyone who does anything with vectors should watch this. ▶ this video