Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique
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 ele...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/1/10 |
| _version_ | 1797410405593645056 |
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| author | Amirul Aizad Ahmad Fuad Tahir Ahmad |
| author_facet | Amirul Aizad Ahmad Fuad Tahir Ahmad |
| author_sort | Amirul Aizad Ahmad Fuad |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T04:28:29Z |
| format | Article |
| id | doaj.art-2270a6c4f88f4ad1ada93e9e96a5b1dc |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T04:28:29Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-2270a6c4f88f4ad1ada93e9e96a5b1dc2023-12-03T13:37:36ZengMDPI AGAxioms2075-16802021-01-011011010.3390/axioms10010010Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition TechniqueAmirul Aizad Ahmad Fuad0Tahir Ahmad1Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, MalaysiaDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai 81310, MalaysiaThis 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.https://www.mdpi.com/2075-1680/10/1/10Jordan-Chevalley decompositionKrohn-Rhodes decompositionelectroencephalography signals |
| spellingShingle | Amirul Aizad Ahmad Fuad Tahir Ahmad Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique Axioms Jordan-Chevalley decomposition Krohn-Rhodes decomposition electroencephalography signals |
| title | Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique |
| title_full | Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique |
| title_fullStr | Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique |
| title_full_unstemmed | Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique |
| title_short | Decomposing the Krohn-Rhodes Form of Electroencephalography (EEG) Signals Using Jordan-Chevalley Decomposition Technique |
| title_sort | decomposing the krohn rhodes form of electroencephalography eeg signals using jordan chevalley decomposition technique |
| topic | Jordan-Chevalley decomposition Krohn-Rhodes decomposition electroencephalography signals |
| url | https://www.mdpi.com/2075-1680/10/1/10 |
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