I have a square matrix $X$ expressed as follows:
where $U_1$ and $U_3$ are real, Is it possible to set the matrices $U2$ and $U_4$ to make $X X' = I$? for example, let's take the matrix $X$ with size $16$ x $16$, the matrix $[U_2; \ \ U_4]$ is a matrix of size $16$ x $4$. In short, $U_1$ and $U_3$ are given and they are real, and $U_2$ and $U_4$ can be changed