When the dimensional complexity of the chemical reaction mechanism arises, it needs special arrangements to deal with such issues. We propose an effective linear algebraic technique to split a complex reaction mechanism into different reaction completion routes to overcome this complexity. Here, three key matrices, the molecular, stoichiometric, and Horiuti matrices, are discussed in detail to deal with the whole mechanism as well as the different reaction routes. The C-matrix procedure is based on calculating the Reduced Row Echelon Form (RREF) for reducing each augmented matrix. This approach is efficient to find the typical results in chemical kinetics and engineering of chemical reactions, i.e., reaction routes, key, and non-key components, key and non-key elements, dependent and independent reaction steps, and overall reaction free from the catalyst. This procedure is very useful to develop new software tools for analyzing complex chemical networks.

当化学反应机理的尺寸复杂性出现时，它需要特殊的布置来处理这些问题。我们提出了一种有效的线性代数技术，将复杂的反应机理分为不同的反应完成路径，以克服这种复杂性。在这里，详细讨论了三个关键矩阵，分子，化学计量和Horiuti矩阵，以处理整个机理以及不同的反应路线。C矩阵过程基于计算减少行梯形形式（RREF）来减少每个扩充矩阵的过程。这种方法可以有效地找到化学动力学和化学反应工程中的典型结果，例如反应路线，关键和非关键组成部分，关键和非关键元素，相关和独立的反应步骤，整个反应过程中没有催化剂。此过程对于开发用于分析复杂化学网络的新软件工具非常有用。