The matrices in the MPS ansatz are not unique, one can, for instance, insert B − − 1 B in the middle of A s i A s i + 1 , then define A ~ ~ s i = A s i B − − 1 and A ~ ~ s i + 1 = B A s i + 1 , and the state will stay unchanged. Such gauge freedom is employed to transform the matrices into a canonical form. Three types of canonical form exist: (1) left-normalized form, when