Lorentzian matrix multiplication and the motions on Lorentzian plane

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