Assume that we have this equation
$$PA=LU$$
Where $A \in \Re^{mxn}$, $L \in \Re^{mxn}$ is a lower triangular matrix and $U \in \Re^{nxn}$ is an upper triangular matrix. $P \in \Re^{mxm}$ is the partial pivoting matrix.
In this case, $A,U,L$ are known. How can I find $P$?
Can I take
$$P = LUA^{\dagger}$$
?