Graphical Linear Algebra
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 way on numbers is close to geometry; the method is full of many proofs and demonstrations that are made with geometric figures.
Fibonacci, preface to Liber Abaci
(first published 1202, 1228 manuscript translated by Lawrence E. Sigler)
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Graphical linear algebra is a work in progress, and there are many open research threads. We are looking for PhD students, so please consider applying!
This blog is written in English. To read and contribute to translations (Dutch, French, German,…) see this page by Vincent Verheyen.
Introduction
Episode 1 – Makélélé and Linear Algebra
Episode 2 – Methodology, Handwaving and Diagrams
Adding and Copying
Episode 3 – Adding (Part 1) and Mr Fibonacci
Episode 4 – Dumbing Down and Magic Lego
Episode 5 – Spoilers, Adding (Part 2) and Zero
Episode 6 – Crema di Mascarpone and Diagrammatic Reasoning
Episode 7 – Copying, Discarding and The Slogan
Episode 8 – When Adding met Copying…
Episode 9 – Natural numbers, diagrammatically
Matrices and PROPs
Episode 10 – Paths and Matrices
Episode 11 – From Diagrams to Matrices
Episode 12 – Monoidal Categories and PROPs (Part 1)
Episode 13 – PROPs (Part 2) and Permutations
Episode 14 – Homomorphisms of PROPs
Episode 15 – Matrices, diagrammatically
Episode 16 – Trust the Homomorphism, for it is Fully Faithful
Integers and Relations
Episode 17 – Maths with Diagrams
Episode 18 – Introducing the Antipode
Episode 19 – Integer matrices
Episode 20 – Causality, Feedback and Relations
Episode 21 – Functions and Relations, diagrammatically
Episode 22 – The Frobenius Equation
Episode 23 – Frobenius Snakes and Spiders
Fractions and Spaces
Episode 24 – Bringing it all together
Episode 25 – Fractions, diagrammatically
Episode 26 – Keep Calm and Divide by Zero
Episode 27 – Linear Relations
Episode 28 – Subspaces, diagrammatically
Episode 29 – Dividing by zero to invert matrices
Episode 30 – The essence of graphical linear algebra
Redundancy – A trilogy by Jason Erbele
Episode R1 – Redundancy and Zebra Snakes
Interlude – string diagrams and resource-sensitive syntax
Sequences and Signal Flow Graphs
Episode 31 – Fibonacci and sustainable rabbit farming
Out of order (for now)
Contributions
Determinants and the Lindström-Gessel-Vienot Lemma – by Solomon Maina
Offtopic
Sometimes this blog actually looks like a blog.
16 September 2016 – Leicester and the battle for universities
16 April 2017 – …, a monoid is a category, a category is a monad, a monad is a monoid, …
10 May 2017 – 1st Workshop on String Diagrams in Computation, Logic, and Physics
3 October 2018 – ACT 2018 – Applied Category Theory Research School
