I am a graduate assistant and was asked a question about FLTs (Mobius Transformations). The student was asked to prove that any FLT can be written as an FLT with determinant 1.(adsbygoogle = window.adsbygoogle || []).push({});

However, I can't make sense of that. If I look at the possible Jordan Canonical forms of 2-by-2's, it would seem that the matrix

[x 0]

[0 y]

where x and y are distinct eigenvalues cannot be represented as an FLT with determinant 1 (since it would require finding a complex number that when multiplied with both x and y gives 1 which violates the uniqueness of multiplicative inverse).

Am I thinking about this the wrong way, or was there a typo in the problem?

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# Fractional Linear Transformation Question

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