Why use a tensor density transformation when doing a coordinate transformations? What is the advantage? I've always learn that transforming a tensor involves pre and post multiplying by the transformation tensor and it's inverse respectively, but I've come across ones in my research that use the tensor density approach which weights the tensor transformation, and would like to know the justification for using the tensor density. I've looked all over the net and I can only find the pure definition of a tensor density, but not why it's used especially over non weighted transformations. Can anyone add insight?