A New Method to Obtain Pythagorean Triple Preserving Matrices

Abstract

Another method to obtain Pythagorean Triple Preserving Matrices is proposed and a singular case is put in evidence. Also, a possible connection with physics is sketched by proving that the set of these matrices is a group. In the last section, we generalize our method to Weighted Pythagorean Triple Preserving Matrices. An interesting open problem is generated by the fact that this type of matrix appears as a product of two matrices of order 4 with a form suggesting quaternions.