Representing Matrices Using Algebraic ZX-calculus

10/13/2021
by   Quanlong Wang, et al.
0

Elementary matrices play an important role in linear algebra applications. In this paper, we represent all the elementary matrices of size 2^m×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×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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset