Corollary 2

Let E₁, E₂ be two finitely generated projective C-modules, u₁ an endomorphism of E₁ and u₂ an endomorphism of E₂; then

By linearity, it suffices to consider the case where u₁ is of the form $x_1 \mapsto \langle x_1, x_1^* \rangle y_1$ and u₂ of the form $x_2 \mapsto \langle x_2, x_2^* \rangle y_2$; then the image of $x_1 \otimes x_2$ under $u_1 \otimes u_2$ is by definition

$x_1^* \otimes x_2^*$ being canonically identified under $\mu$ with an element of $(E_1 \otimes E_2)^*$. As $\langle y_1 \otimes y_2, x_1^* \otimes x_2^* \rangle = \langle y_1, x_1^* \rangle \langle y_2, x_2^* \rangle$, formula (26) follows in this case from (17).