Decomposing the Krohn-Rhodes form of electroencephalography (EEG) signals using Jordan-Chevalley decomposition technique

• Main Authors: Ahmad Fuad, Amirul Aizad, Ahmad, Tahir
• Format: Article
• Published: MDPI AG 2021
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/94925/; http://dx.doi.org/10.3390/axioms10010010
• Institution: Universiti Teknologi Malaysia

This paper explores how electroencephalography (EEG) signals in the Krohn-Rhodes form can be decomposed further using the Jordan-Chevalley decomposition technique. First, the recorded EEG signals of a seizure were transformed into a set of matrices. Each of these matrices was decomposed into its elementary components using the Krohn-Rhodes decomposition method. The components were then further decomposed into semisimple and nilpotent matrices using the Jordan-Chevalley decomposition. These matrices—which are the extended building blocks of elementary EEG signals—provide evidence that the EEG signals recorded during a seizure contain patterns similar to that of prime numbers.