Lie Group Property of Generalized Linear Deformation Transformation

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Tuğrul F.

ICOMAA 2023 6th International HYBRID Conference on Mathematical Advances and Applications, İstanbul, Türkiye, 13 Mayıs 2023, ss.97-98, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.97-98
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this study, using the definition of linear anisotropic transformation in 3-dimensional Euclidean space 𝐸3, we have defined a linear generalized deformation transformation. Unlike homothetic rotation matrices, we have shown that this transformation consists of the product of different expansion (or shrinkage) and different infinitesimal orthogonal matrices for each 𝑥 ∈ ℝ3 and 𝜆1, 𝜆2, 𝜆3 ∈ ℝ+ scalars. We have shown that matrix B is a regular matrix and that this set of matrices has a group structure. We examined the Lie group structure of this group.