# How to solve matrix function in Matlab?

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Qiaohairuo Lin on 21 Feb 2021
Commented: John D'Errico on 21 Feb 2021
Hi all! I'm faced with the following question:
X=AXB+C
where A is a 4*4 matrix, B is a 3*3 matrix, X and C are 4*3 matrices. I know the values of A, B and C. How can I solve out X using matlab?
John D'Errico on 21 Feb 2021
inv(A)*X + X*(-B) = inv(A)*C
help sylvester
SYLVESTER Solve Sylvester Equation. X = SYLVESTER(A,B,C) solves the Sylvester equation A*X + X*B = C, where A is a m-by-m matrix, B is a n-by-n matrix, and X and C are m-by-n matrices. Documentation for sylvester doc sylvester

Paul Hoffrichter on 21 Feb 2021
Edited: Paul Hoffrichter on 21 Feb 2021
Define Z = AXB + C - X
You have to start off with your initial best guess for X based upon the nature of the model. For lack of any information, guess that X_0 = C. (Then Z = ACB.)
Create a Q = cost function for Z. You could try the trace of Z, and then check to see if Z has all entries close to 0.
You then need to find a zero crossing of your cost function. To do this, you can use fzero.
Other initial guesses may result in different answers if there are multiple roots.

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