# Tensor transformations for change of coordinate system

by aeson25
Tags: coordinate, tensor, transformations
 P: 7 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: $$\mathbf{Q'}= \frac {\mathbf{M} \times \mathbf{Q} \times \mathbf{M}^T}{det(\mathbf{M})}$$ Where Q is the tensor in question and M is the transformation matrix and M^T is the transpose of M. Does anyone know why the difference?
 Sci Advisor P: 1,563 Such on object is properly called a "tensor density". Specifically, it is a "tensor density of weight -1", since the determinant appears with the power -1.
 P: 7 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.