Algebraic algorithms for eigen-problems of a reduced biquaternion matrix and applications
In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new a...
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| Vydáno v: | Applied mathematics and computation Ročník 463; s. 128358 |
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15.02.2024
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| Abstract | In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n×n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem.
•The eigen-problems of reduced biquaternion matrices are further studied based on the complex representation form.•Propose new algebraic algorithms for finding the eigenvalues and the eigenvectors of a reduced biquaternion matrix.•An n×n reduced biquaternion matrix has infinite eigenvalues.•There are multiple eigenvalues corresponding to the same eigenvector of a reduced biquaternion matrix.•The proposed method is more comprehensive and can find more eigenvalues of a reduced biquaternion matrix. |
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| AbstractList | In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n×n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem.
•The eigen-problems of reduced biquaternion matrices are further studied based on the complex representation form.•Propose new algebraic algorithms for finding the eigenvalues and the eigenvectors of a reduced biquaternion matrix.•An n×n reduced biquaternion matrix has infinite eigenvalues.•There are multiple eigenvalues corresponding to the same eigenvector of a reduced biquaternion matrix.•The proposed method is more comprehensive and can find more eigenvalues of a reduced biquaternion matrix. |
| ArticleNumber | 128358 |
| Author | Guo, Zhenwei Wang, Gang Jiang, Tongsong Vasil'ev, V.I. |
| Author_xml | – sequence: 1 givenname: Zhenwei orcidid: 0000-0002-0165-9363 surname: Guo fullname: Guo, Zhenwei organization: Institute of Mathematics and Information Science, North-Eastern Federal University, Yakutsk 677000, Russia – sequence: 2 givenname: Tongsong surname: Jiang fullname: Jiang, Tongsong email: jiangtongsong@sina.com organization: School of Electronic Information, Shandong Xiandai University, Jinan Shandong 250104, PR China – sequence: 3 givenname: Gang surname: Wang fullname: Wang, Gang organization: Institute of Mathematics and Information Science, North-Eastern Federal University, Yakutsk 677000, Russia – sequence: 4 givenname: V.I. surname: Vasil'ev fullname: Vasil'ev, V.I. email: vasvasil@mail.ru organization: Institute of Mathematics and Information Science, North-Eastern Federal University, Yakutsk 677000, Russia |
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| Cites_doi | 10.1007/s00006-007-0056-5 10.1007/s00006-013-0391-7 10.1007/s00006-006-0002-y 10.4134/JKMS.2007.44.6.1313 10.1016/j.geomphys.2005.02.004 10.1007/s00006-014-0449-1 10.1063/1.1769106 10.1007/BF01443559 10.1109/TSP.2004.828901 10.1002/mma.6135 10.1109/TCSI.2008.920068 10.1016/j.neucom.2018.09.023 10.1080/03081087.2018.1439878 10.1007/s00006-006-0010-y 10.1007/s11045-013-0268-x 10.1088/1751-8113/44/7/072001 10.18514/MMN.2015.1421 10.1016/j.cpc.2018.03.021 10.1088/0305-4470/33/15/306 10.1007/s00521-014-1578-0 |
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Appl. doi: 10.1007/s00521-014-1578-0 |
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