Matrix Theory on Lorentz-Minkowski Scalar Product

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. [1] B. O’ Neill, Semi-Riemannian Geometry. With Applications to Relativity, Academic Press, Inc., New York, 1983.
2. [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. [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. [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. [5] S. Y¨uce, Linear Algebra (4th Edition), Pegem Academy, Istanbul, 2022.