Thanks! I should also have mentioned that, assuming we've got an m x n matrix acting by multiplying vectors fed to it on the right, dimension squashing is guar

Thanks! I should also have mentioned that, assuming we've got an m x n matrix acting by multiplying vectors fed to it on the right, dimension squashing is guaranteed only if n is less than m, not whenever they are unequal. (I guess one could argue that, in the case where n is greater than m, dimension squashing happens if you feed in vectors on the left.)