Suppose I have objects which are rotations of d-dimensional real vectors with an additional optional scaling.(adsbygoogle = window.adsbygoogle || []).push({});

Concatenating means multiplication of these objects.

I want to define an addition operator, so that the "sum" of two rotations gives another unique rotation with scalings only.

Which other assumptions do I need to show that only certain dimensions for the vectors are possible (under some conditions for division algebras d=2,4?; i.e. complex numbers and quaternions)? I suppose rotations already have some of the required properties?!

Will the addition operation be neccessarily the one of complex numbers and quaternions?

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# Algebra for rotations

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