Cool Logic

Leo Lobski (ILLC)

An Introduction to Graphical Linear Algebra (or how to do rigorous mathematics with wires and boxes)

February 15th at 18:00, in F1.15

We introduce the graphical language of string diagrams, which allow us to reason about mathematical structures by drawing pictures. Specifically, we use string diagrams to define monoids and comonoids, and demonstrate how the matrices of natural numbers arise from interactions between a monoid and a comonoid. By studying a certain class of categories known as PROPs, we will see that the diagrammatic approach is in fact in one-to-one correspondence with the algebraic one. We proceed to outline how this generalises to matrices with rational entries, thus recasting all of the (rational, finite-dimensional) linear algebra in terms of string diagrams.