> This is mostly a bunch of notes to myself
As Bessis has described in his book [1], it is extremely difficult to understand math someone else has written. The words and symbols dont convey imagery or ideas that the author has in their mind. I was surprised to read in that book that this applied to mathematicians just as it applies to you and I.
Coming back to this article, I wish it were written in the spirit of the essence of linear algebra [2] - conveying the essences in images and pictures instead of words. I am curious to hear from others if they feel this way or is it just me.
[1] Mathematica: A Secret World of Intuition and Curiosity
[2] Essence of linear algebra (3Blue1Brown, youtube)
> In general, given two finite-dimensional vector spaces U and W, then U ≃ W exactly when dim(U)=dim(W).
Is that really true? I don’t think it is. Specifically surely at least they have to be vector spaces either over the same field or over fields which are themselves isomorphic. I’m thinking say U is a vector space over R and W is a vector space over Q. Dim(U) = Dim(W)=1 but U and W are not isomorphic because there exists no bijection between the reals and the rationals.I think that part should've been "vector subspaces" rather than vector spaces since that is how U and W are defined in the paragraph prior.
I'll add this as a note, thanks!
Thanks for reading though!
hopefully you also enjoy the next one which imo makes a fun connection between the linear algebraic CRT and the fourier transform :)