This paper aims to generate primitive triples using the matrix of components obtained upon the sides of right-angled triangles (Pythagorean triples), where sequences of primitive integers p, q, and h represents the right-angled triangle sides difference, sum, and hypotenuse, respectively and the sides of this triangle odd leg u, even leg e and the hypotenuse h are defined by a pair of positive integer indices (i, j) where i is an odd number, and j is an even number.

This paper aims to generate primitive triples using the matrix of components obtained upon the sides of right-angled triangles (Pythagorean triples), where sequences of primitive integers p, q, and h represents the right-angled triangle sides difference, sum, and hypotenuse, respectively and the sides of this triangle odd leg u, even leg e and the hypotenuse h are defined by a pair of positive integer indices (i, j) where i is an odd number, and j is an even number.