Here's a rather verbose series of blog posts that's intended to introduce linear algebra to beginners in an unusual way.
Here's a rather verbose series of blog posts that's intended to introduce linear algebra to beginners in an unusual way.
In this blog we will explore a very different way of understanding linear algebra, where the standard concepts such as matrices, vector spaces and bases will feature very rarely. We will also touch on applications of linear algebra in this new light.
It's hard to get a feel of the content since the post titles aren't perfectly descriptive in traditional linear algebra terminology. From skimking the first dozen ish posts it feels like he is...
It's hard to get a feel of the content since the post titles aren't perfectly descriptive in traditional linear algebra terminology. From skimking the first dozen ish posts it feels like he is building a LA motivation, that yes while graphical, is ultimately motivating the subject without relying on determinants and the unintuitive proof chain leading to eigenvalues. I'm curious how well it might mesh with Linear Algebra Done Right.
I wish I would have time to read the posts in depth, but I'm focused on other projects. I also wonder if there is style overlap with "an illustrated guide to linear programming." I've read about 15 or so linear algebra texts over the years back when I was more involved in maths, and have a fondness for the subject, though I mostly ended up focusing on linear optimization and convex analysis.
When I come up for air next spring I'll have to read these posts in more detail!
Having read further, he seems to be using an approach based on category theory. The diagrams he starts with are isomorphic to matrices of natural numbers. Later he introduces an operator...
Having read further, he seems to be using an approach based on category theory. The diagrams he starts with are isomorphic to matrices of natural numbers. Later he introduces an operator (antipode) which multiplies by -1, to get matrixes of integers. And then introduces the 'i' operator to get matrices of complex integers.
There are proofs showing that these things really are isomorphic, that I skipped over.
After doing a lot of skimming, he eventually gets to relations and fractions. (At this point I'm not really comprehending anymore, but it seems pretty elegant.)
I saw the mention of category theory on the home page and chuckled but didn't look closer. Not a lot of people go deep into category theory. Like you a skimmed through, but since he is inventing...
I saw the mention of category theory on the home page and chuckled but didn't look closer. Not a lot of people go deep into category theory. Like you a skimmed through, but since he is inventing his own visual notation, you only get so much from a skim.
Here's a rather verbose series of blog posts that's intended to introduce linear algebra to beginners in an unusual way.
It's hard to get a feel of the content since the post titles aren't perfectly descriptive in traditional linear algebra terminology. From skimking the first dozen ish posts it feels like he is building a LA motivation, that yes while graphical, is ultimately motivating the subject without relying on determinants and the unintuitive proof chain leading to eigenvalues. I'm curious how well it might mesh with Linear Algebra Done Right.
I wish I would have time to read the posts in depth, but I'm focused on other projects. I also wonder if there is style overlap with "an illustrated guide to linear programming." I've read about 15 or so linear algebra texts over the years back when I was more involved in maths, and have a fondness for the subject, though I mostly ended up focusing on linear optimization and convex analysis.
When I come up for air next spring I'll have to read these posts in more detail!
Having read further, he seems to be using an approach based on category theory. The diagrams he starts with are isomorphic to matrices of natural numbers. Later he introduces an operator (antipode) which multiplies by -1, to get matrixes of integers. And then introduces the 'i' operator to get matrices of complex integers.
There are proofs showing that these things really are isomorphic, that I skipped over.
After doing a lot of skimming, he eventually gets to relations and fractions. (At this point I'm not really comprehending anymore, but it seems pretty elegant.)
I saw the mention of category theory on the home page and chuckled but didn't look closer. Not a lot of people go deep into category theory. Like you a skimmed through, but since he is inventing his own visual notation, you only get so much from a skim.
Cheers!