Do pseudovectors also transform differently to vectors under spatial dilation, not just reflections and parity? It is frequently expressed online that the only difference between vectors and pseudovectors is a change in sign with reflection/parity transformations etc.
For instance the pseudovector angular momentum $\vec L=\vec r\wedge \vec p$ keeps the same direction under parity inversion while the vectors $\vec r$ and $\vec p$ change sign.
However is it not also true that under spatial dilation transformations, the pseudovector angular momentum would stretch by $\kappa^2$ (if $\vec r\rightarrow\kappa \vec r$ and $\vec p=m \frac{d \vec r}{dt} \rightarrow m \frac{d (\kappa \vec r)}{dt}=\kappa \vec p$) while the vectors $\vec r$ and $\vec p$ only stretch by $\kappa$? So it isn't just the difference under parity transformations etc?
 A: Well, one possibility is that this is just a matter of where attention is focused. Since, excluding the weak force, all physical laws are invariant under parity, it's interesting to note that pseudovectors transform differently than vectors under that operation. However, real physics isn't, as far as we know, invariant under spatial dilations, and so for most people this isn't an interesting (approximate) symmetry and likely not included in the mental set of operations one could apply to vectors or pseudovectors. Perhaps researchers of conformal field theory have a different point of view.
A second point is that $\vec{L} = \vec{r} \times \vec{p}$ is just one equation for one pseudovector. By dimentional anslysis, the angular momenentum is proportional to the length scale squared, and so this double-dilation could be viewed as just its dimensional properties. Pseudovectors are, more technically, elements of the exterior algebra of a vector space, whose basis elements are the wedge products of basis elements of the regular vector space. Since physical space has dimensions, so do its basis elements, and thus the basis elements of the exterior algebra are dimensionfull as well.
