1. bookVolume 30 (2022): Edition 1 (February 2022)
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eISSN
1844-0835
Première parution
17 May 2013
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access type Accès libre

A Study on Commutative Elliptic Octonion Matrices

Publié en ligne: 12 Mar 2022
Volume & Edition: Volume 30 (2022) - Edition 1 (February 2022)
Pages: 151 - 169
Reçu: 07 May 2021
Accepté: 15 Aug 2021
Détails du magazine
License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
Abstract

In this study, firstly notions of similarity and consimilarity are given for commutative elliptic octonion matrices. Then the Kalman-Yakubovich s-conjugate equation is solved for the first conjugate of commutative elliptic octonions. Also, the notions of eigenvalue and eigenvector are studied for commutative elliptic octonion matrices. In this regard, the fundamental theorem of algebra and Gershgorin’s Theorem are proved for commutative elliptic octonion matrices. Finally, some examples related to our theorems are provided.

Keywords

MSC 2010

[1] F.A. Aliev, V.B. Larin, Optimization of linear control systems, Chemical Rubber Company Press, USA, 1998. Search in Google Scholar

[2] J.C. Baez, The octonions, Bulletin of the American Mathematical Society 39 (2001), 145-205.10.1090/S0273-0979-01-00934-X Search in Google Scholar

[3] D. Calvetti, L. Reichel, Application of ADI iterative methods to the restoration of noisy images, SIAM Journal on Matrix Analysis and Applications 17 (1996), 165-186.10.1137/S0895479894273687 Search in Google Scholar

[4] A. Cihan, M.A. Güngör, Commutative octonion matrices, 9th International Eurasian Conference on Mathematical Sciences and Applications, Skopje, 2020. Search in Google Scholar

[5] A. Sürekçi, M.A. Güngör, Commutative elliptic octonions, 10th International Eurasian Conference on Mathematical Sciences and Applications, Turkey, 2021. Search in Google Scholar

[6] P.J. Daboul, R. Delbourga, Matrix representation of octonions and generalizations, Journal of Mathematical Physics 40 (1999), 4134-4150.10.1063/1.532950 Search in Google Scholar

[7] M. Dehghan, M. Hajarian, Efficient iterative method for solving the second-order Sylvester matrix equation EV F2 − AV F − CV = BW, IET Control Theory and Applications 3 (2009) 1401-1408.10.1049/iet-cta.2008.0450 Search in Google Scholar

[8] L. Dieci, M.R. Osborne, R.D. Russe, A Riccati transformation method for solving linear BVPs. I: Theoretical Aspects, SIAM Journal on Numerical Analysis 25 (1998), 1055-1073.10.1137/0725061 Search in Google Scholar

[9] W.H. Enright, Improving the efficiency of matrix operations in the numerical solution of sti ordinary differential equations, ACM Transactions on Mathematical Software 4 (1978), 127-136.10.1145/355780.355784 Search in Google Scholar

[10] M.A. Epton, Methods for the solution of AXD − BXC = E and its applications in the numerical solution of implicit ordinary differential equations, BIT Numerical Mathematics 20 (1980), 341-345.10.1007/BF01932775 Search in Google Scholar

[11] F.R. Gantmacher, The theory of matrices, Chelsea Publishing Company, New York, 1959. Search in Google Scholar

[12] H.H. Kösal, On the commutative quaternion matrices, Ph.D. Thesis, Sakarya University, 2016. Search in Google Scholar

[13] A. Jameson, Solution of the equation ax + xb = c by inversion of an m × m or n × n matrix, SIAM Journal on Applied Mathematics 16 (1968), 1020-1023.10.1137/0116083 Search in Google Scholar

[14] Y. Song, Conttruction of commutative number systems, Linear and Multilinear Algebra 2020.10.1080/03081087.2020.1801568 Search in Google Scholar

[15] E. Souza, S.P. Bhattacharyya, Controllability, observability and the solution of ax − xb = c, Linear Algebra and its Applications 39 (1981), 167-188.10.1016/0024-3795(81)90301-3 Search in Google Scholar

[16] Y. Tian, Matrix representations of octonions and their applications, Advances in Applied Clifford Algebras 10 (2000), 61-90.10.1007/BF03042010 Search in Google Scholar

[17] Y. Tian, Similarity and consimilarity of elemants in the real Cayley-Dickson algebras, Advances in Applied Clifford Algebras 9 (1999), 61-76.10.1007/BF03041938 Search in Google Scholar

[18] A. Wu, E. Zhang, F. Liu, On closed-form solutions to the generalized Sylvester-conjugate matrix equation, Applied Mathematics and Computation 218 (2012), 9730-9741.10.1016/j.amc.2012.03.020 Search in Google Scholar

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