Matrix Division of two 4x1 matrices to get a 4x4 matrix

I have three matrices: S, Sprime, and M. They are:

Sprime = [0.5; 0.5; 0; 0];

S = [1; 0; 0; 1];

M = 0.5*[1, 1, 0, 0; ...
         1, 1, 0, 0; ...
         0, 0, 0, 0; ...
         0, 0, 0, 0]; ...

In the equation: Sprime = M*S, the math works out... M*S == S. However, I'm having trouble solving for M and getting the same matrix shown above. Is this possible? Or is it too arbitrary for some reason?.

Answer 1

[James Tursa]

In general there will be no unique solution for M if the only thing you have to start with is S and Sprime. If you think about it, that is 4 equations and 16 unknowns. So using various methods in MATLAB may yield a solution that will not match what you started with.