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Graphical Linear Algebra
Personal blog · graphicallinearalgebra.netmathprogramming
Graphical Linear Algebra is a personal blog at graphicallinearalgebra.net about math and programming. Since 2015, 32 different Hacker News readers have linked it 54 times, most often “Graphical linear algebra: from matrices to monoids”. The last post was in 2021, but the archive is still widely read.
Applications are open for the ACT Applied Category Theory Research School 2018! And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this
Most-linked posts?
- Graphical linear algebra: from matrices to monoids13 people · 13 mentions · first linked 2018-02-16
- /4 people · 5 mentions · first linked 2016-07-07
- Graphical Linear Algebra3 people · 3 mentions · first linked 2015-04-29
- Graphical Linear Algebra2 people · 2 mentions · first linked 2015-05-19
- /about/2 people · 2 mentions · first linked 2020-12-02
- String Diagrams for Linear Algebra2 people · 2 mentions · first linked 2019-05-17
- Introducing the Antipode2 people · 2 mentions · first linked 2015-07-01
- /2015/05/06/crema-di-mascarpone-rules-of-the-game-part-2-and-diagrammatic-reasoning/2 people · 2 mentions · first linked 2018-02-17
What Hacker News says?
You might enjoy https://graphicallinearalgebra.net/ . The author uses Legos to describe algebras and diagrams to describe symmetric monoidal categories.
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on “Conversations with a six-year-old on functional programming”Submitted Graphical linear algebra: from matrices to monoids as a story · 317 points
HN discussionYou'd probably like this then: https://graphicallinearalgebra.net
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on “Matrix Multiplication”Submitted Graphical Linear Algebra as a story · 304 points
HN discussionIf you feel comfortable with Math A but not Math B you might enjoy _Graphical Linear Algebra_[1], which is specifically that bridge! As someone who is decent at Math B but mostly incompetent at Math A I suspect it comes down to the old analysis vs algebra opposition — being better at thinking about things visually/spatially vs linguistically. Both are trainable though. I think the approach outlined here works well e…
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on “I rewired my brain to become fluent in math (2014)”Submitted Graphical Linear Algebra as a story · 287 points
HN discussionAlso nice: Erik Meijer Explains it well: https://www.youtube.com/watch?v=JMP6gI5mLHc (check out FP101 on edx) Statebox guys doing stuff with category theory, blockchain and petrinets: https://www.youtube.com/user/wires0 https://statebox.org/ Graphical linear algebra: https://graphicallinearalgebra.net/ Jules Hedges working on game theory : https://julesh.com/
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on “An invitation to category theory”Submitted A monoid is a category, a category is a monad, a monad is a monoid as a story · 156 points
HN discussionAnd here is linear algebra as path counting [1]. This is closely related to path integrals in quantum physics. The rules for combining quantum amplitudes are the rules for combining path counts [2]. This is also how graphical linear algebra works [3]. And since we are all hackers here, if you replace the underlying number system with the min-sum semiring you get things like Dijkstra's algorithm. I really like how al…
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on “The Art of Linear Algebra [pdf]”Submitted String Diagrams for Linear Algebra as a story · 142 points
HN discussionThere was a web book I found a while ago that built up some sort of motivation for linear algebra. Unfortunately I don't remember what it was or the title. Edit: found it, https://graphicallinearalgebra.net Ymmv. Matrix multiplication is defined the way it is imo because it has interesting properties that way. Not very satisfying though.
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on “Linear Algebra for AI”Submitted Graphical Linear Algebra as a story · 93 points
HN discussionReally interesting. As well he seems to re-derive and implementation of Forth. In episode 6, Right under the diagran for Crema di Marscapone he has a formula. Does anyone that uses Forth know if it has that circle-plus operator? It seems to really lend to conciseness - and I hadn't remembered anything like it last time I looked at Forth. https://graphicallinearalgebra.net/2015/05/06/crema-di-masca...
Comment linking /2015/05/06/crema-di-mascarpone-rules-of-the-game-part-2-and-diagrammatic-reasoning/
on “Graphical linear algebra: from matrices to monoids”Submitted Matrices, diagrammatically as a story · 47 points
HN discussionIt's interesting how some of these diagrams are almost equivalent in the context of encoding computation in interaction nets using symmetric interaction combinators [1]. From the perspective of the lambda calculus for example, the duplication of the addition node in "When Adding met Copying" [2] mirrors exactly the iterative duplication of lambda terms - ie. something like (λx.x x) M! [1]: https://ezb.io/thoughts/in…
Comment linking /2015/05/12/when-adding-met-copying/
on “Graphical Linear Algebra”Submitted Introducing the Antipode as a story · 20 points
HN discussionPawel Sobocinski, in collaboration with Filippo Bonchi and Fabio Zanasi https://graphicallinearalgebra.net/about/
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on “Graphical Linear Algebra”Submitted Integer matrices with string diagrams as a story · 16 points
HN discussion> More importantly, I would like to point out that string diagrams are not standard. They're standard in category theory, which is what the series is about. > precisely because it is not standard and not needed for most (any?) useful mathematical work. Uh oh, you better let everyone using it know, especially all those pesky type theorists. > When I read articles by category theory boosters, I get the sense (rightly…
Comment linking /2015/04/30/spoilers-adding-part-2-and-zero/
on “Graphical Linear Algebra”Submitted Graphical Linear Algebra – Bringing it all together as a story · 12 points
HN discussion> "math-lite" The series is intended for a general audience and starts by laying the groundwork necessary for exposition of this paper: [1]. Article 4 [2] explains why it is introduced this way. > end up just rehashing standard mathematics in opaque ways It's just an explanation of string diagrams [3][4], pretty transparent and standard. I find it funny that your response to this is so similar to that of the abacist…
Comment linking /2015/04/26/adding-part-1-and-mr-fibonacci/
on “Graphical Linear Algebra”Submitted Causality, Feedback and Relations as a story · 10 points
HN discussionI kind of agree with you (especially on "math-lite category theory" being upvoted by people who read it and feel smart for understanding it), but I think the point has slightly been missed. The blog is a sort of side project, a popular treatment of the linear algebra stuff coming out of the "real research", which is applying the string diagrams to find graphical, compositional axiomatisations of concurrent systems.…
Comment linking /2016/09/07/31-fibonacci-and-sustainable-rabbit-farming/
on “Graphical Linear Algebra”Submitted Functions and relations, diagrammatically as a story · 5 points
HN discussionAnother cool use of diagrams in abstract algebra: https://graphicallinearalgebra.net
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on “Why Feynman Diagrams Are So Important”Submitted The Frobenius equation as a story · 3 points
HN discussionWhat are LEGOs good for? They are good for explaining Graphical Linear Algebra: https://graphicallinearalgebra.net/2015/04/29/dumbing-down-m...
Comment linking /2015/04/29/dumbing-down-magic-lego-and-the-rules-of-the-game-part-1/
on “Lego IKEA Bygglek – First Look”Submitted Graphical Linear Algebra as a story · 2 points
HN discussionThere's also graphical linear algebra which takes matrices into a more category theory interpetation that is also visual: https://graphicallinearalgebra.net
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on “Viewing Matrices and Probability as Graphs”Submitted Keep Calm and Divide by Zero as a story · 2 points
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