The Matrix Pythagorean Equation over GL2(Z)
Hongjian Li, Weilin Zhang
Abstract
In this paper, we study the ordered solutions of the matrix Pythagorean equation X2+Y2=Z2 over GL2(Z) . Exploiting the independent sign symmetry of the equation, we first reduce the full solution set to the trace-nonnegative subset M, consisting of those solutions for which all three traces are nonnegative. We then determine a canonical decomposition of M into orbits under simultaneous integral conjugacy.
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