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we are given a 2×2 matrix [itex]S[/itex] such that [itex]det(S)=1[/itex].

I would like to find a 2x2 invertible matrix [itex]A[/itex] such that: [itex]A S A^{-1} = R[/itex], where [itex]R[/itex] is an orthogonal matrix.

Note that the problem can be alternatively reformulated as: Is it possible to decompose a matrixS∈SL(2,ℝ)in the following way: [tex]S=A^{-1}R A [/tex]where R is orthogonal and A is invertible?

Is this a well-known problem? To be honest, I don't have many ideas on how to tackle this problem, so even a suggestion that could get me on the right track would be very welcome.

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# I Question about decomposition of matrices in SL(2,R)

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