Is this property the intuition behind 3D editors inversing objects when the scale becomes negative? Is it possible to pick such vectors u and v such that this reflection happens in shearing as well?
Is additional negative scaling terms/reflections something we need to worry when we move into homogeneous coordinates or up to higher dimensions?
Just want to comment that I noticed negative scaling matrix=multiplying 2 reflection matrix=180 degree rotation matrix
So does "orientation" only have two options ("forward" and "backwards") in all dimensions?
can we think this like all points move to its mirrored position which cause the shape as like a bag inside-out and we see its inner faces outside