Korean J. Math. Vol. 31 No. 3 (2023) pp.295-303
DOI: https://doi.org/10.11568/kjm.2023.31.3.295

Geometric applications and kinematics of umbrella matrices

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Published: Sep 30, 2023
Keywords:
Umbrella matrix, Orthogonal matrix, Darboux matrix, Infinitesimal motion.
Mathematics Subject Classification:
70B15, 15B10, 53A17

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Mert Çarboğa
Department of Mathematics, Ankara University, Ankara, 06100, Turkey.
https://orcid.org/0000-0003-0938-0348
Yusuf Yaylı
Department of Mathematics, Ankara University, Ankara, 06100, Turkey.

Abstract

This paper introduces a novel method for obtaining umbrella matrices, which are defined as orthogonal matrices with row sums of one, using skew-symmetric matrices and Cayley’s Formula. This method is presented for the first time in this paper. We also investigate the kinematic properties and applications of umbrella matrices, demonstrating their usefulness as a tool in geometry and kinematics. Our findings provide new insights into the connections between matrix theory and geometric applications.



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