As soon as I got back into graduate physics, I started noticing transforms of matrix operators that looked like this: A is the original matrix operator A prime is the matrix operator transformed by gamma. Gamma is any kind of vector transformation. It might be a rotation, or a change of coordinate system, (from Cartesian to polar for example).. Presented in this manner, the origins of the transform, A acting on gamma and the product acted upon by the inverse of gamma didn't make any sense to me. I found an article, (I'll try to get a reference up here soon), that gave a very detailed very academic explanation, but it was still no good for me. Recently, a professor finally went through the steps that arrive at the above. It was short concise, and made sense! Here they are. Gamma is a matrix that transforms a vector into another vector, say... x prime into x. I mentioned that already. The inverse of gamma will convert an x vec...