Recorded electroencephalography (EEG) signals can be represented as square matrices, which have been extensively analyzed using mathematical methods to extract invaluable information concerning brain functions in terms of observed electrical potentials; such information is critical for diagnosing brain disorders. Several studies have revealed that certain such square matrices—in particular, those related to so-called “elementary EEG signals”—exhibit properties similar to those of prime numbers in which every square EEG matrix can be regarded as a composite of these signals. A new approach to ordering square matrices is pivotal to extending the idea of square matrices as composite numbers. In this paper, several ordering concepts are investigated and a new technique for ordering matrices is introduced. Finally, some properties of this matrix order are presented, and the potential applications of this technique to analyzing EEG signals are discussed.

中文翻译：

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新型先验算子对转换后的记录脑电图（EEG）信号的排序

记录的脑电图（EEG）信号可以表示为方阵，已使用数学方法对其进行了广泛分析，以根据观察到的电势提取有关脑功能的宝贵信息；此类信息对于诊断脑部疾病至关重要。多项研究表明，某些此类平方矩阵，尤其是与所谓的“基本EEG信号”有关的平方矩阵，其展示性质与质数相似，其中每个平方EEG矩阵都可以视为这些信号的合成。对平方矩阵进行排序的新方法对于扩展平方矩阵作为合成数的概念至关重要。本文研究了几种排序概念，并介绍了一种用于排序矩阵的新技术。最后，