How Can I Solve Matrix Equation in Matlab

Question

Say I have the following matrix equation

X - B*X*C = D

Where,
X: 3 by 5, to be solved;
B: 3 by 3;
C: 5 by 5;
D: 3 by 5;

Is there any convenient method that I can use for solving the system? fsolve?

Answer 1

In case B or C are invertible, you can check the matrix cookbook section 5.1.10 deals with similar settings:

X * inv(C) - B * X = D * inv(C)

Can be translated to

x = inv( kron( eye, -B ) + kron( inv(C)', eye ) ) * d

where x and d are vector-stack of X and D respectively.

Answer 2

You can use MATLAB's dlyap function:

X = dlyap(B,C,D)