Structural analysis of Pythagorean monoids

This article reports on studies of the structure of a monoid  [image omitted] that consists of all linear transformations which map Pythagorean triples into Pythagorean triples. A detailed description of the elements of  [image omitted] the monoid with all LPTs whose rank is 1, is given. An open problem is discussed and a partial answer given. The results of this analysis will be of interest to a broad spectrum of readers. It bridges such concepts as fixed point, linear transformation, and Pythagorean triple. It should be of pedagogical as well as theoretical value.