I'm reading book in classical physics where it mentioned that, quote:
" the transformation matrix (of two different cartesian coordinate systems) was orthogonal, so the transformation was reflection or a rotation (Goldstein, Poole, and Safko,2002)".
I was thinking that for a reflection along an axis(say y=x) of a 2D plane(say x-y plane) was equivalent as the rotation along $(y=x,z)$ in a 3D space.
My question was that:
In Euclidean space, could all the reflection in a low dimension space being written as a rotation in higher dimension space?
Further, if it was true, could it be applied to any other metric space? That was, could all the reflection tensor being written as a rotation tensor.