How to Solve a linear matrix equation of an array $M = BMC$ where $ B$ and $C$ are known Adding to the question's description : 
I am doing Feature extraction from videos and i am trying to implement this one line of mathematical equation to matlab or even any algorithm .
let's say I have $ B $ and $ C $ which are $ 10 ×10$ matrices 


*

*$ R $ is also a $ 10 × 10 $ matrix but it should satisfy two conditions* 


1) $M = B×M×C$
2) The Values in $ M $ should be within a given range [$x$( which is min) $y$(max)] given by the user 
i can handle the constraints of the range but i have no idea on how to proceed with the 1st condition at all , much less converting it into matlab
I have found several solutions to this type of problem
1)Sylvester's equation which approximates $ AX+XB = C $ or $AX + XB + C = 0 $
2)Lyapunov Matrix equation which approximates $AX+XA'+Q = 0$
both of these implementations of matlab i have found in this link given below 
https://github.com/ajt60gaibb/freeLYAP
but i need help in the mathematics area as to how i can use those (if i can) to  $M = BMC$

If you multiply the equation $M = BMC$ by the inverse of $B$ on both sides and take everything on the same side of the equal sign, you get $$ B^{-1} M - MC = 0.$$
This is a Sylvester equation where the last term is the null matrix (all elements equal to zero). You should be able to solve your problem in Matlab by using lyap(inv(B),-C,zeros(10,10)) (here it should be ok to use the inv command because you are dealing with 10 x 10 matrices, consider another way of inverting $B$ if you also need to solve the same problem for bigger ones).
