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)

If you like this blog, please subscribe to get email updates when new articles are published. You will find a subscription link at the bottom of this page.

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

Why string diagrams?

Sequences and Signal Flow Graphs

Episode 31 – Fibonacci and sustainable rabbit farming

Out of order (for now)

Orthogonality and projections

Eigenstuff, diagrammatically

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