A Pythagorean Triple Preserving Matrix (PTPM) is a $3 \times 3$ matrix such that if it is multiplied by a Pythagorean Triple, the result is also a Pythagorean Triple. Necessary and sufficient conditions for a Pythagorean Triple Preserving Matrix to be symmetric are given. Monoids of Symmetric Pythagorean Triple Preserving Matrices (SPTPM) with positive integer entries will be developed, and to ensure that the set is closed under matrix multiplication, the focus will be on finding commutative SPTPM's.
"Symmetric Pythagorean Triple Preserving Matrices." Missouri J. Math. Sci. 13 (1) 4 - 16, Winter 2001. https://doi.org/10.35834/2001/1301004