MATLAB: How to solve matrix equation for variable inside a summation? Analytical or numerical.

MATLABmatrixmatrix equationsolvesolve equation

Hello together

is there a chance to solve the following matrix equation for X?

where all Ai and D are known. X is of course constant over iteration, but unknown. All are 6×6 matrices.

I would be happy on any hint of any analytical, numerical, or what so ever solution.

Thank you!

Hello,

There are several ways that you can apply. Here, I just show you an example how to solve this problem by using solve function in matlab

clear
A = [1 2; 3 4]
syms x1 x2 x3 x4
X = [x1 x2; x3 x4]
B = A*X*A'
D = [1 0; -2 3]
sol = solve(B==D)
sol.x1
sol.x2
sol.x3
sol.x4

In this case, I assume that "n = 1", A, X, D are 4x4 matrices, but you can extend for 6x6 or larger and different n.

Hope it could help you.

You may create x vector symbolically by writing

x=sym('x',[N 1]);

Then, solve the equation by writing

x=inv(a)*b;

Hope this helps.

Well, the approach would be as follows:

n=30;
x=sym(zeros(1,n));%preallocation
syms t
for i=1:n
   x(i)=str2sym(sprintf('x%d(t)',i));
end

Now, you can easily take derivative of x as

 diff(x,t)

and observe the result you want.