i dont get the point of pseudovectors. the only example I ever see is the cross product, and their reasoning is that it should still be defined as the determinant of the matrix with the basis vectors on top, the components of the first vector in the second row, and the components of the second vector in the third row. so if you define it this way, it will not be invariant under a coordinate transform that changes the handedness of the system (ie, a reflection). then they say that since in real life the coordinate system obviously doesnt matter, you have to be careful in defining physical quanities in terms of cross products, like the magnetic field and angular velocity. So why not just define cross products to be normal vectors in the first place? The only example ive seen of a pseudotensor is the levi-cevita symbol, which is another way of defining the cross product. thats really circular reasoning, at least in my opinion.