Solution
= Solution
Equality of the mixed <derivatives> gives
$$
-U_y\Phi+UV\Phi=-V_x\Phi+VU\Phi.
$$
For a fundamental <matrix> solution this is equivalent to the <zero-curvature condition>
$$
\boxed{V_x-U_y+[U,V]=0}.
$$
= Solution
Equality of the mixed <derivatives> gives
$$
-U_y\Phi+UV\Phi=-V_x\Phi+VU\Phi.
$$
For a fundamental <matrix> solution this is equivalent to the <zero-curvature condition>
$$
\boxed{V_x-U_y+[U,V]=0}.
$$