Elementary matrices play an important role in linear algebra applications. In this paper, we develop and implement (in \texttt{discopy}) an algorithm to 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 [arXiv:2007.13739]. We show how this representation method could be used for representing symmetrising projectors which are essential in AKLT states. By doing so we pave the way towards visualising by string diagrams important matrix technologies deployed in AI especially machine learning.
翻译：在线性代数应用中, 基本矩阵在线性代数应用中起着重要作用 。 在本文中, 我们开发并实施一项算法( 以\ textt{ disscopy} ), 以使用代数 ZX 计算仪代表所有基本矩阵, 大小为 $2\m\ times 2\ m=m=m。 然后我们用 ZX 计算仪的重写规则在反向显示其属性并转换。 因此, 我们能够通过字符串图绘制任何大小为 2\m\ times 2 ⁇ n$ 的矩阵, 而不采用[ arXiv: 2007. 13739] 中显示的矩阵的图表格式。 我们展示了该表达法如何用来代表对AKLT 各州至关重要的相配对的投影仪。 这样我们就能为通过字符串图来直观地展示在AI 特别是机器学习中应用的重要矩阵技术铺平了道路 。
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