Matrix Theory on Lorentz-Minkowski Scalar Product

Year 2024, Volume: 14 Issue: 2, 65 - 78, 31.07.2024

Ata Marangoz Salim Yüce

Abstract

In this paper, we investigate Lorentz-Minkowski matrix multiplication introduced in [3] by O. Ke¸cilio˘glu and H. G¨undo˘gan. Unlike [3], we will define some
transformations to get a connection between Lorentz-Minkowski matrix multiplication
and Euclidean matrix multiplication which allows for a more practical use instead of
direct approach.

Keywords

pseudo matrix multiplication, isomorphism, Euclidean matrix

References

• [1] B. O’ Neill, Semi-Riemannian Geometry. With Applications to Relativity, Academic Press, Inc., New York, 1983.
• [2] H. G¨undo˘gan, O. Ke¸cilio˘glu, Lorentzian matrix multiplication and the motions on Lorentzian plane, Glasnik Matematicki, 41(2), 2006, 329-334.
• [3] H. G¨undo˘gan, O. Ke¸cilio˘glu, Pseudo Matrix Multiplication, Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 66(2), 2017, 37-43.
• [4] H. G¨undo˘gan, O. Ke¸cilio˘glu, Generalized matrix multiplication and its some application, Acta Universitatis. Series: Mathematics and Informatics, 32(5), 2017, 789-798.
• [5] S. Y¨uce, Linear Algebra (4th Edition), Pegem Academy, Istanbul, 2022.