Geometry of dual umbrella matrices

M. Çarboğa, Y. Yaylı

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 3-dimensional Euclidean space and obtained the rotation angle and translation amount associated with this motion. Furthermore, we showed that these matrices are Circulant matrices.

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 3 (2023), pp. 77-87