Among these norms, again the L_2 norm stands out. It being the standard measure of distance. Here, it is important because it is invariant under rotation. We ca

Among these norms, again the L_2 norm stands out. It being the standard measure of distance. Here, it is important because it is invariant under rotation. We can define rotation without any appeal to length as the "special linear group". This consists of all matrices that have determinant 1. I wonder where exactly the connection between 'rotation invariance' and 'estimate of the expected value' comes from.