# Estimating a matrix from another matrix

The problem is the non- negative matrix factorization of a matrix. Let me explain my problem I have an original matrix $A=\begin{bmatrix} 0.248437 &0.25198098 & 0.25396825 & 0.25077881\\ 0.253125& 0.25198098& 0.24761904 &0.24766355\\ 0.248437& 0.24722662& 0.24920634& 0.24766355\\ 0.25& 0.24881141& 0.24920634& 0.25389408 \end{bmatrix}$ and I have a matrix $B=\begin{bmatrix} 0.38331781& 0.385229& 0.384043 &0.381118\\ 0.37776086& 0.377539& 0.381224 &0.381850\\ 0.29993458& 0.300691& 0.298606 &0.299959\\ 0.34108473& 0.337021& 0.335967 &0.337317 \end{bmatrix}$. What I know is that the matrix $B$ is some scaled version of $A$ i.e $PD$ where $P$ is a permutation matrix and $D$ is a diagonal matrix. Can i somehow get an approximation of $A$ from $B$ if I retain some properties of $A$ like the maximum of each row and minimum of each row to get an idea of how much scaling has been done, similarly if I keep a record of each column sum , and its maximum and minimum value. My main question is can I estimate my $A$ from $B$ by keeping some parameters with me beforehand. Can somebody help or suggest some text for this.