- #1
mnb96
- 715
- 5
Hello,
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 matrix S∈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.
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 matrix S∈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.