Glasnik Matematicki, Vol. 41, No.2 (2006), 329-334.

LORENTZIAN MATRIX MULTIPLICATION AND THE MOTIONS ON LORENTZIAN PLANE

Halit Gündogan and Osman Kecilioglu

Abstract.   In this paper, a new matrix multiplication is defined in R_n^m × R_pⁿ by using Lorentzian inner product in Rⁿ, where R_n^m is set of matrices of m rows and n columns. With this multiplication it has been shown that R_nⁿ is an algebra with unit. By means of orthogonal matrices with respect to this multiplication, coordinate transformations are defined on n-dimensional Lorentz space Lⁿ. As a special case, motions on L² Lorentz plane are obtained.

2000 Mathematics Subject Classification.   51M05, 53A17.

Key words and phrases.   Lorentz space, rotation, reflection.

DOI: 10.3336/gm.41.2.15

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