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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| Published in: | Applied mathematics and computation Vol. 463; p. 128358 |
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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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| References | Pei, Chang, Ding (br0210) 2004; 52 Isokawa, Nishimura, Matsui (br0220) 2010 Catoni, Cannata, Zampetti (br0270) 2006; 16 Kula, Yayl (br0090) 2007; 44 Jiang, Zhang, Jiang (br0140) 2018; 229 br0320 Zhang, Guo, Wang, Jiang (br0310) 2020; 43 De Leo, Scolarici (br0110) 2000; 33 Gai, Yang, Wan, Wang (br0200) 2015; 26 Catoni (br0170) 2008; 18 Pei, Chang, Ding, Chen (br0180) 2008; 55 Kösal, Tosun (br0240) 2014; 24 Hamilton (br0010) 1840; 2 Kamberov, Norman, Pedit, Pinkall (br0050) 2002 Kobayashi (br0230) 2018; 320 Cao (br0150) 2022 Erdoğdu, Özdemir (br0120) 2013; 23 Gai, Wan, Wang, Yang (br0190) 2014; 25 Adler (br0030) 1995 Özdemir, Ergin (br0100) 2006; 56 Jiang (br0130) 2004; 45 Catoni, Cannata, Zampetti (br0250) 2006; 16 Kösal, Kyiǧit, Tosun (br0280) 2015; 16 Rodman (br0060) 2014 Cao, Tang (br0300) 2021; 41 Kösal, Tosun (br0290) 2019; 67 Cockle (br0020) 1849; 35 Moiseyev (br0070) 2011 Segre (br0160) 1892; 40 Conway, Smith (br0040) 2003 Brody, Graefe (br0080) 2011; 44 Kösal, Tosun (br0260) 2017; 25 Gai (10.1016/j.amc.2023.128358_br0190) 2014; 25 Cockle (10.1016/j.amc.2023.128358_br0020) 1849; 35 Catoni (10.1016/j.amc.2023.128358_br0270) 2006; 16 Kösal (10.1016/j.amc.2023.128358_br0240) 2014; 24 Erdoğdu (10.1016/j.amc.2023.128358_br0120) 2013; 23 Kula (10.1016/j.amc.2023.128358_br0090) 2007; 44 Hamilton (10.1016/j.amc.2023.128358_br0010) 1840; 2 Kamberov (10.1016/j.amc.2023.128358_br0050) 2002 Rodman (10.1016/j.amc.2023.128358_br0060) 2014 Conway (10.1016/j.amc.2023.128358_br0040) 2003 Özdemir (10.1016/j.amc.2023.128358_br0100) 2006; 56 Cao (10.1016/j.amc.2023.128358_br0150) Jiang (10.1016/j.amc.2023.128358_br0130) 2004; 45 Jiang (10.1016/j.amc.2023.128358_br0140) 2018; 229 Kösal (10.1016/j.amc.2023.128358_br0280) 2015; 16 Pei (10.1016/j.amc.2023.128358_br0210) 2004; 52 Brody (10.1016/j.amc.2023.128358_br0080) 2011; 44 Zhang (10.1016/j.amc.2023.128358_br0310) 2020; 43 Gai (10.1016/j.amc.2023.128358_br0200) 2015; 26 Kobayashi (10.1016/j.amc.2023.128358_br0230) 2018; 320 Moiseyev (10.1016/j.amc.2023.128358_br0070) 2011 De Leo (10.1016/j.amc.2023.128358_br0110) 2000; 33 Pei (10.1016/j.amc.2023.128358_br0180) 2008; 55 Isokawa (10.1016/j.amc.2023.128358_br0220) 2010 Kösal (10.1016/j.amc.2023.128358_br0260) 2017; 25 Segre (10.1016/j.amc.2023.128358_br0160) 1892; 40 Kösal (10.1016/j.amc.2023.128358_br0290) 2019; 67 Adler (10.1016/j.amc.2023.128358_br0030) 1995 Catoni (10.1016/j.amc.2023.128358_br0250) 2006; 16 Catoni (10.1016/j.amc.2023.128358_br0170) 2008; 18 Cao (10.1016/j.amc.2023.128358_br0300) 2021; 41 |
| References_xml | – volume: 24 start-page: 769 year: 2014 end-page: 779 ident: br0240 article-title: Commutative quaternion matrices publication-title: Adv. Appl. Clifford Algebras – volume: 320 start-page: 150 year: 2018 end-page: 156 ident: br0230 article-title: Twin-multistate commutative quaternion Hopfield neural networks publication-title: Neurocomputing – ident: br0320 – volume: 26 start-page: 307 year: 2015 end-page: 320 ident: br0200 article-title: Denoising color images by reduced quaternion matrix singular value decomposition publication-title: Multidimens. Syst. Signal Process. – volume: 18 start-page: 9 year: 2008 end-page: 28 ident: br0170 article-title: Commutative (Segre's) quaternion fields and relation with Maxwell equations publication-title: Adv. Appl. Clifford Algebras – volume: 16 start-page: 1 year: 2006 end-page: 28 ident: br0250 article-title: An introduction to commutative quaternions publication-title: Adv. Appl. Clifford Algebras – volume: 41 start-page: 441 year: 2021 end-page: 453 ident: br0300 article-title: Algebraic properties of reduced biquaternions publication-title: J. Math. Res. Appl. – volume: 33 start-page: 2971 year: 2000 ident: br0110 article-title: Right eigenvalue equation in quaternionic quantum mechanics publication-title: J. Phys. A, Math. Gen. – volume: 44 start-page: 1313 year: 2007 end-page: 1327 ident: br0090 article-title: Split quaternions and rotations in semi Euclidean space publication-title: J. Korean Math. Soc. – volume: 229 start-page: 1 year: 2018 end-page: 7 ident: br0140 article-title: Algebraic techniques for eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic mechanics publication-title: Comput. Phys. Commun. – volume: 35 start-page: 434 year: 1849 end-page: 437 ident: br0020 article-title: On systems of algebra involving more than one imaginary; and on equations of the fifth degree publication-title: Lond. Edinb. Philos. Mag. J. Sci. – volume: 25 start-page: 125 year: 2017 end-page: 142 ident: br0260 article-title: Some equivalence relations and results over the commutative quaternions and their matrices publication-title: An. Ştiinţ. Univ. ‘Ovidius’ Constanţa, Ser. Mat. – year: 2003 ident: br0040 article-title: On Quaternions and Octonions – volume: 52 start-page: 2012 year: 2004 end-page: 2031 ident: br0210 article-title: Commutative reduced biquaternions and their Fourier transform for signal and image processing applications publication-title: IEEE Trans. Signal Process. – year: 2011 ident: br0070 article-title: Non-Hermitian Quantum Mechanics – volume: 25 start-page: 945 year: 2014 end-page: 954 ident: br0190 article-title: Reduced quaternion matrix for color texture classification publication-title: Neural Comput. Appl. – start-page: 1 year: 2010 end-page: 6 ident: br0220 article-title: Commutative quaternion and multistate Hopfield neural networks publication-title: The 2010 International Joint Conference on Neural Networks (IJCNN) – volume: 67 start-page: 926 year: 2019 end-page: 938 ident: br0290 article-title: Universal similarity factorization equalities for commutative quaternions and their matrices publication-title: Linear Multilinear Algebra – volume: 16 start-page: 965 year: 2015 end-page: 977 ident: br0280 article-title: Consimilarity of commutative quaternion matrices publication-title: Miskolc Math. Notes – volume: 43 start-page: 3513 year: 2020 end-page: 3523 ident: br0310 article-title: Algebraic techniques for least squares problems in commutative quaternionic theory publication-title: Math. Methods Appl. Sci. – volume: 55 start-page: 2673 year: 2008 end-page: 2685 ident: br0180 article-title: Eigenvalues and singular value decompositions of reduced biquaternion matrices publication-title: IEEE Trans. Circuits Syst. I, Regul. Pap. – volume: 23 start-page: 615 year: 2013 end-page: 623 ident: br0120 article-title: On eigenvalues of split quaternion matrices publication-title: Adv. Appl. Clifford Algebras – volume: 16 start-page: 85 year: 2006 end-page: 101 ident: br0270 article-title: An introduction to constant curvature spaces in the commutative (Segre) quaternion geometry publication-title: Adv. Appl. Clifford Algebras – year: 2014 ident: br0060 article-title: Topics in Quaternion Linear Algebra – volume: 44 year: 2011 ident: br0080 article-title: On complexified mechanics and coquaternions publication-title: J. Phys. A, Math. Theor. – volume: 2 start-page: 424 year: 1840 end-page: 434 ident: br0010 article-title: On a new species of imaginary quantities, connected with the theory of quaternions publication-title: Proc. R. Ir. Acad. – volume: 56 start-page: 322 year: 2006 end-page: 336 ident: br0100 article-title: Rotations with unit timelike quaternions in Minkowski 3-space publication-title: J. Geom. Phys. – volume: 40 start-page: 413 year: 1892 end-page: 467 ident: br0160 article-title: The real representations of complex elements and extension to bicomplex systems publication-title: Math. Ann. – year: 2022 ident: br0150 article-title: On left spectrum of a split quaternionic matrix – year: 1995 ident: br0030 article-title: Quaternionic Quantum Mechanics and Quantum Fields – year: 2002 ident: br0050 article-title: Quaternions, Spinors, and Surfaces – volume: 45 start-page: 3334 year: 2004 end-page: 3338 ident: br0130 article-title: An algorithm for eigenvalues and eigenvectors of quaternion matrices in quaternionic quantum mechanics publication-title: J. Math. Phys. – volume: 18 start-page: 9 year: 2008 ident: 10.1016/j.amc.2023.128358_br0170 article-title: Commutative (Segre's) quaternion fields and relation with Maxwell equations publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-007-0056-5 – volume: 2 start-page: 424 year: 1840 ident: 10.1016/j.amc.2023.128358_br0010 article-title: On a new species of imaginary quantities, connected with the theory of quaternions publication-title: Proc. R. Ir. Acad. – year: 1995 ident: 10.1016/j.amc.2023.128358_br0030 – volume: 23 start-page: 615 year: 2013 ident: 10.1016/j.amc.2023.128358_br0120 article-title: On eigenvalues of split quaternion matrices publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-013-0391-7 – volume: 16 start-page: 1 year: 2006 ident: 10.1016/j.amc.2023.128358_br0250 article-title: An introduction to commutative quaternions publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-006-0002-y – year: 2011 ident: 10.1016/j.amc.2023.128358_br0070 – volume: 44 start-page: 1313 issue: 6 year: 2007 ident: 10.1016/j.amc.2023.128358_br0090 article-title: Split quaternions and rotations in semi Euclidean space E24 publication-title: J. Korean Math. Soc. doi: 10.4134/JKMS.2007.44.6.1313 – volume: 56 start-page: 322 issue: 2 year: 2006 ident: 10.1016/j.amc.2023.128358_br0100 article-title: Rotations with unit timelike quaternions in Minkowski 3-space publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2005.02.004 – ident: 10.1016/j.amc.2023.128358_br0150 – volume: 25 start-page: 125 issue: 3 year: 2017 ident: 10.1016/j.amc.2023.128358_br0260 article-title: Some equivalence relations and results over the commutative quaternions and their matrices publication-title: An. Ştiinţ. Univ. ‘Ovidius’ Constanţa, Ser. Mat. – volume: 24 start-page: 769 year: 2014 ident: 10.1016/j.amc.2023.128358_br0240 article-title: Commutative quaternion matrices publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-014-0449-1 – volume: 35 start-page: 434 issue: 238 year: 1849 ident: 10.1016/j.amc.2023.128358_br0020 article-title: On systems of algebra involving more than one imaginary; and on equations of the fifth degree publication-title: Lond. Edinb. Philos. Mag. J. Sci. – volume: 45 start-page: 3334 issue: 8 year: 2004 ident: 10.1016/j.amc.2023.128358_br0130 article-title: An algorithm for eigenvalues and eigenvectors of quaternion matrices in quaternionic quantum mechanics publication-title: J. Math. Phys. doi: 10.1063/1.1769106 – volume: 40 start-page: 413 year: 1892 ident: 10.1016/j.amc.2023.128358_br0160 article-title: The real representations of complex elements and extension to bicomplex systems publication-title: Math. Ann. doi: 10.1007/BF01443559 – volume: 52 start-page: 2012 issue: 7 year: 2004 ident: 10.1016/j.amc.2023.128358_br0210 article-title: Commutative reduced biquaternions and their Fourier transform for signal and image processing applications publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2004.828901 – volume: 43 start-page: 3513 issue: 6 year: 2020 ident: 10.1016/j.amc.2023.128358_br0310 article-title: Algebraic techniques for least squares problems in commutative quaternionic theory publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.6135 – volume: 55 start-page: 2673 issue: 9 year: 2008 ident: 10.1016/j.amc.2023.128358_br0180 article-title: Eigenvalues and singular value decompositions of reduced biquaternion matrices publication-title: IEEE Trans. Circuits Syst. I, Regul. Pap. doi: 10.1109/TCSI.2008.920068 – volume: 320 start-page: 150 year: 2018 ident: 10.1016/j.amc.2023.128358_br0230 article-title: Twin-multistate commutative quaternion Hopfield neural networks publication-title: Neurocomputing doi: 10.1016/j.neucom.2018.09.023 – volume: 67 start-page: 926 issue: 5 year: 2019 ident: 10.1016/j.amc.2023.128358_br0290 article-title: Universal similarity factorization equalities for commutative quaternions and their matrices publication-title: Linear Multilinear Algebra doi: 10.1080/03081087.2018.1439878 – volume: 16 start-page: 85 year: 2006 ident: 10.1016/j.amc.2023.128358_br0270 article-title: An introduction to constant curvature spaces in the commutative (Segre) quaternion geometry publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-006-0010-y – year: 2003 ident: 10.1016/j.amc.2023.128358_br0040 – volume: 26 start-page: 307 year: 2015 ident: 10.1016/j.amc.2023.128358_br0200 article-title: Denoising color images by reduced quaternion matrix singular value decomposition publication-title: Multidimens. Syst. Signal Process. doi: 10.1007/s11045-013-0268-x – volume: 44 issue: 7 year: 2011 ident: 10.1016/j.amc.2023.128358_br0080 article-title: On complexified mechanics and coquaternions publication-title: J. Phys. A, Math. Theor. doi: 10.1088/1751-8113/44/7/072001 – start-page: 1 year: 2010 ident: 10.1016/j.amc.2023.128358_br0220 article-title: Commutative quaternion and multistate Hopfield neural networks – year: 2014 ident: 10.1016/j.amc.2023.128358_br0060 – volume: 16 start-page: 965 issue: 2 year: 2015 ident: 10.1016/j.amc.2023.128358_br0280 article-title: Consimilarity of commutative quaternion matrices publication-title: Miskolc Math. Notes doi: 10.18514/MMN.2015.1421 – year: 2002 ident: 10.1016/j.amc.2023.128358_br0050 – volume: 229 start-page: 1 year: 2018 ident: 10.1016/j.amc.2023.128358_br0140 article-title: Algebraic techniques for eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic mechanics publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2018.03.021 – volume: 33 start-page: 2971 issue: 15 year: 2000 ident: 10.1016/j.amc.2023.128358_br0110 article-title: Right eigenvalue equation in quaternionic quantum mechanics publication-title: J. Phys. A, Math. Gen. doi: 10.1088/0305-4470/33/15/306 – volume: 41 start-page: 441 issue: 5 year: 2021 ident: 10.1016/j.amc.2023.128358_br0300 article-title: Algebraic properties of reduced biquaternions publication-title: J. Math. Res. Appl. – volume: 25 start-page: 945 year: 2014 ident: 10.1016/j.amc.2023.128358_br0190 article-title: Reduced quaternion matrix for color texture classification publication-title: Neural Comput. 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| Title | Algebraic algorithms for eigen-problems of a reduced biquaternion matrix and applications |
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