To the author's credit, he has this in the first line, ie, that the article was not intended for others to read and enjoy.
> 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)
There are lots of people who write math in a way that is very easy for others (of an appropriate level of experience let’s say) to understand. I also didn’t find this particularly hard to follow, although some of it is I think a little fast and loose. eg
> 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.
Fair on all accounts! Surely, this could be made way more lively if I were in front of a blackboard waving my hands and drawing images, but alas, the medium is what it is :)
To the author's credit, he has this in the first line, ie, that the article was not intended for others to read and enjoy.
> 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)
There are lots of people who write math in a way that is very easy for others (of an appropriate level of experience let’s say) to understand. I also didn’t find this particularly hard to follow, although some of it is I think a little fast and loose. eg
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.yes, definitely some of it is (purposefully) fast and loose, though (ideally!) mostly unambiguous with reasonable assumptions
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!
It’s a cool article. I love linear algebra, particularly in settings like the polynomials.
ha, thank you! it's very fun to write these
hopefully you also enjoy the next one which imo makes a fun connection between the linear algebraic CRT and the fourier transform :)
I don't want everything to be images and pictures. Often, I enjoy words for communicating math.
Fair on all accounts! Surely, this could be made way more lively if I were in front of a blackboard waving my hands and drawing images, but alas, the medium is what it is :)
Thanks for reading though!