Question: is there an analogue concept of a pseudovector (axial vector) but for matrices?
The motivation is something like this:
A vector field F(r) transforms under a "rotation" g via gF(r) = (gF)(g^{-1}r); a pseudovector does the same, but incorporates an additional factor det(g).
A "matrix field" M(r) transforms similarly like gM(r)g^{-1} = (RM(g^{-1}r)R^{-1}), with R denoting a matrix-representation of g.
Now, if I have a matrix field that has an additional factor of det(g) that then seems very analogous to the pseudovector concept.
