= F. J. M. Barning
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<F. J. M. Barning> gave a matrix-based generation process for <primitive Pythagorean triples>. His 1963 Mathematisch Centrum report verifies the initials and presents three <unimodular matrices> generating all such triples without repetition, with a fixed leg-order convention.<Over Pythagorese en bijna-Pythagorese driehoeken en een generatieproces met behulp van unimodulaire matrices by F. J. M. Barning>[Title page and section 1, pp. 3–5]{ref}
The transformations preserve the equation $x^2+y^2=z^2$. Starting from $(4,3,5)$, with the even leg first, repeated transformations build a branching tree of solutions. The method turns a <Diophantine equation> into a recursive enumeration algorithm with a uniqueness theorem.<Over Pythagorese en bijna-Pythagorese driehoeken en een generatieproces met behulp van unimodulaire matrices by F. J. M. Barning>[Generation theorem and proof]{ref}
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