メービウス変換について
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概要
- 論文の詳細を見る
A Mobius transformation f, which is a composition of a finite number of reflections in (n-1)-planes or inversions in (n-1)-spheres in R^n, can always be expressed in one of the following forms: f(x)=rA(x)+a or f(x)=I_c(rA(x)+a) where r>0, a∈R^n, c∈R^n, A∈O (n) and I_c is the inversion with respect to a unit sphere around some point c. It seems that the above fact is well-known but its proof is not familiar. In this note, we give an elementary proof of the above property.
- 北陸大学の論文