Reel Kuaterniyon Matrislerinin Bazı Yeni Özellikleri ve Matlab Uygulamaları

Yıl 2019, Cilt: 40 Sayı: 1, 42 - 60, 22.03.2019

Kemal Gökhan Nalbant Salim Yüce

https://doi.org/10.17776/csj.425691

Öz

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.

Anahtar Kelimeler

Kuaterniyonlar, reel kuaterniyonlar, reel kuaterniyon matrisler, reel matris temsili, determinant, blok matrisler

Some New Properties of The Real Quaternion Matrices and Matlab Applications

Öz

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.

Anahtar Kelimeler

Quaternions, real quaternions, real quaternion matrices, real matrix representation, determinant, block matrices, block matrices

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