Representing Matrices Using Algebraic ZX-calculus

Elementary matrices play an important role in linear algebra applications. In this paper, we represent all the elementary matrices of size 2^m\times 2^m using algebraic ZX-calculus. Then we show their properties on inverses and transpose using rewriting rules of ZX-calculus. As a consequence, we are able to depict any matrices of size 2^m\times 2^n by string diagrams without resort to a diagrammatic normal form for matrices as shown in [Wang 2020]. By doing so we pave the way towards visualising by string diagrams important matrix technologies deployed in AI especially machine learning.