Year 2019, Volume 40, Issue 1, Pages 42 - 60 2019-03-22

Reel Kuaterniyon Matrislerinin Bazı Yeni Özellikleri ve Matlab Uygulamaları
Some New Properties of The Real Quaternion Matrices and Matlab Applications

Kemal Gökhan NALBANT [1] , Salim YÜCE [2]

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Bu çalışmada, ilk olarak,  reel kuaterniyon matrislerin kümesinin  reel matris halkası üzerinde boyutlu bir modül olduğu ve kompleks matris halkası üzerinde  boyutlu bir modül olduğu gösterilmiştir. Ayrıca, reel kuaterniyon matrislerin bazı yeni özellikleri tanımlanmıştır. Daha sonra, reel kuaterniyon matrislerin matris temsilleri Matlab uygulamaları ile kolayca elde edilmiştir. Bu matrisler reel kuaterniyon matrislerin tersini bulmak için de uygulanmış ve bu matrislerle ters matrisler kolaylıkla elde edilmiştir. Buna ek olarak, reel kuaterniyon matrislerin matris temsilleri için bazı yeni özellikler bulunmuştur. Ayrıca, tipindeki reel kuaterniyon blok matrislerin tersi yeni yöntemlerle elde edilmiştir. Son olarak,  tipindeki reel kuaterniyon matrislerin determinantını hesaplamak için yeni bir yöntem bulunmuş ve Matlab uygulaması ile bu matrislerin determinantı kolayca hesaplanmıştır.

In this study, firstly, it was shown that the set of real quaternion matrices  is a -dimensional module over the real matrix ring  and -dimensional module over the complex matrix ring . Moreover, some new properties of the real quaternion matrices were described. Then, matrix representations of the real quaternion matrices were found easily by Matlab. These matrices were also applied to find the inverse of the real quaternion matrices and inverse matrices were obtained easily with these matrices. In addition, some new properties for matrix representations of the real quaternion matrices were found. Also, the inverse of the  real quaternion block matrices was obtained by new methods. Finally, a new method to calculate the determinant of the  real quaternion matrices was found and the determinant of these matrices was calculated easily with Matlab application.

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Primary Language en
Subjects Basic Sciences
Journal Section Natural Sciences
Authors

Orcid: 0000-0002-5065-2504
Author: Kemal Gökhan NALBANT (Primary Author)
Institution: YILDIZ TEKNİK ÜNİVERSİTESİ, KİMYA-METALURJİ FAKÜLTESİ
Country: Turkey


Orcid: 0000-0002-8296-6495
Author: Salim YÜCE
Institution: YILDIZ TEKNİK ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ
Country: Turkey


Bibtex @research article { csj425691, journal = {Cumhuriyet Science Journal}, issn = {2587-2680}, eissn = {2587-246X}, address = {Cumhuriyet University}, year = {2019}, volume = {40}, pages = {42 - 60}, doi = {10.17776/csj.425691}, title = {Some New Properties of The Real Quaternion Matrices and Matlab Applications}, key = {cite}, author = {NALBANT, Kemal Gökhan and YÜCE, Salim} }
APA NALBANT, K , YÜCE, S . (2019). Some New Properties of The Real Quaternion Matrices and Matlab Applications. Cumhuriyet Science Journal, 40 (1), 42-60. DOI: 10.17776/csj.425691
MLA NALBANT, K , YÜCE, S . "Some New Properties of The Real Quaternion Matrices and Matlab Applications". Cumhuriyet Science Journal 40 (2019): 42-60 <http://dergipark.gov.tr/csj/issue/43798/425691>
Chicago NALBANT, K , YÜCE, S . "Some New Properties of The Real Quaternion Matrices and Matlab Applications". Cumhuriyet Science Journal 40 (2019): 42-60
RIS TY - JOUR T1 - Some New Properties of The Real Quaternion Matrices and Matlab Applications AU - Kemal Gökhan NALBANT , Salim YÜCE Y1 - 2019 PY - 2019 N1 - doi: 10.17776/csj.425691 DO - 10.17776/csj.425691 T2 - Cumhuriyet Science Journal JF - Journal JO - JOR SP - 42 EP - 60 VL - 40 IS - 1 SN - 2587-2680-2587-246X M3 - doi: 10.17776/csj.425691 UR - https://doi.org/10.17776/csj.425691 Y2 - 2019 ER -
EndNote %0 Cumhuriyet Science Journal Some New Properties of The Real Quaternion Matrices and Matlab Applications %A Kemal Gökhan NALBANT , Salim YÜCE %T Some New Properties of The Real Quaternion Matrices and Matlab Applications %D 2019 %J Cumhuriyet Science Journal %P 2587-2680-2587-246X %V 40 %N 1 %R doi: 10.17776/csj.425691 %U 10.17776/csj.425691
ISNAD NALBANT, Kemal Gökhan , YÜCE, Salim . "Some New Properties of The Real Quaternion Matrices and Matlab Applications". Cumhuriyet Science Journal 40 / 1 (March 2019): 42-60. https://doi.org/10.17776/csj.425691