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...
@Studiot
crocque already admitted he made an error on terminology. We're talking about a hexagon circumscribed by a circle. If you don't believe it, see my attached picture for visual confirmation of the 6 triangles, see wiki for verbal confirmation.
@crocque
Are you taking this into...
Of course I tried googling it. I didn't say I didn't find ANY definitions, I said I couldn't find a CLEAR definition which included information pertaining to the entirety of the second sentence of my last post with an emphasis on the parenthetical parts. The online definitions basically say...
I can't seem to find a clear definition of "tensor density" online. How does this differ (or provide an advantage) (practically, not mathematically) from a regular coordinate transformation? FYI, I'm trying to follow the transformation of a anisotropic density (actual matter density) in a paper.
In school I've always learned that tensor transformations took the form of:
\mathbf{Q'}=\mathbf{M} \times \mathbf{Q} \times \mathbf{M}^T
However, in all the recent papers I've been reading. They've been doing the transformation as:
\mathbf{Q'}= \frac {\mathbf{M} \times \mathbf{Q}...