<<Mentor note: This thread has been split from this thread due to going a bit off-topic.>> I would actually disagree with this. Any tensor has well defined units, but its components may not have the same units as the tensor basis may consist of basis tensors with different units. For example, the stress tensor of classical mechanics always has units of pressure, but depending on the chosen basis may have components which do not. If I use unit vectors to describe a velocity, its components have units of length/time, but if I use basis vectors with units of length, the components would have units of 1/time, making the vector units length/time as before. Unfortunately, physics texts often introduce tensors in such a way that the distinction between a tensor and its components in a given basis is not really clear.