Geometry of dual umbrella matrices
ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL, cilt.16, ss.77-87, 2023 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16
- Basım Tarihi: 2023
- Doi Numarası: 10.32513/asetmj/1932200823306
- Dergi Adı: ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.77-87
- Ankara Üniversitesi Adresli: Evet
Özet
Umbrella matrices and their geometry have been studied in works [1, 2, 3], and the generalized form of [3] is addressed in [4]. In this study, for the first time, we obtained Dual Umbrella matrices using the Cayley Formula for Dual skew-symmetric matrices with zero row sums. We provided the relationship between the skew-symmetric matrix and the Darboux matrix of the motion. We demonstrated that Dual Umbrella matrices represent a screw motion in 3dimensional Euclidean space and obtained the rotation angle and translation amount associated with this motion. Furthermore, we showed that these matrices are Circulant matrices.