 Also in characteristic 2 and for matrices with more than two rows the Hamiltonian cycle polynomial isn't changed by adding the "i"-th column to the "j"-th one in a matrix where the "i"-th and "j"-th rows are identical what, particularly, yields the identity

for an "n"×"n"-matrix formula_12, "m"×"m"-matrices formula_34 and diagonal formula_51, "m"×"n"-matrix formula_5 and "n"×"m"-matrix formula_53.This identity's restriction to the case when formula_12 is unitary, formula_55 and formula_56, where formula_14 is the identity "m"×"m"-matrix, makes the (2"m"+"n")×(2"m"+"n")-matrix in the equality's right side unitary and its Hamiltonian cycle polynomial computable, hence, in polynomial time what therefore generalizes the above-given formula for the Hamiltonian cycle polynomial of a unitary matrix.Apart from the above-mentioned compression transformations, in characteristic 2 the following relation is also valid for the Hamiltonian cycle polynomials of a matrix and its partial inverse (for formula_58 and formula_59 being square, formula_58 being invertible)