Ordering of Transformed Recorded Electroencephalography (EEG) Signals by a Novel Precede Operator

Abstract

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.