If two matrices share their eigenvectors, they can be simultaneously diagonalized. In the basis where they are both diagonal, it is clear that their product does not depend on their order because multiplication of diagonal matrices is just multiplication of numbers. The uncertainty principle, by contrast, is an expression of the fact that often two matrices A and B do not always commute, i.e., that AB − BA does not necessarily equal 0. The fundamental commutation relation of matrix mechanics, ∑ ∑ k ( X n k P k m − − P n k X k m ) = i ℏ ℏ δ δ n m implies then that there are no states that simultaneously have a definite position and momentum.