Reel Kuaterniyon Matrislerinin Bazı Yeni Özellikleri ve Matlab Uygulamaları

Bu çalışmada, ilk olarak, Mn H  reel kuaterniyon matrislerin kümesinin Mn   reel matris halkası üzerinde 4 boyutlu bir modül olduğu ve Mn   kompleks matris halkası üzerinde 2 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, 2  2 tipindeki reel kuaterniyon blok matrislerin tersi yeni yöntemlerle elde edilmiştir. Son olarak, 2  2 tipindeki reel kuaterniyon matrislerin determinantını hesaplamak için yeni bir yöntem bulunmuş ve Matlab uygulaması ile bu matrislerin determinantı kolayca hesaplanmıştır.

Some New Properties of The Real Quaternion Matrices and Matlab Applications

In this study, firstly, it was shown that the set of real quaternion matrices   MHn is a 4 -dimensional module over the real matrix ring   M n and 2 -dimensional module over the complex matrixring   M n . Moreover, some new properties of the real quaternion matrices were described. Then, matrixrepresentations of the real quaternion matrices were found easily by Matlab. These matrices were also appliedto 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 2  2 real quaternion block matrices was obtained by new methods. Finally, a new method tocalculate the determinant of the 22 real quaternion matrices was found and the determinant of these matriceswas calculated easily with Matlab application.

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