how to calculate transformation matrix x=A*y

hello,

I'm embarrassed but I can not find a way to calculate a transformation matrix in the form: x=A*y (x-vector rank(n), y-vector rank(n), A-matrix rank(nxn)) I could create symbolic A and solve every row manually, but there must be a simple command for such a simple operation.

Answer 1

[Star Strider]

I would use the pinv function (although I’ll likely hear about it!):

% x=A*y —> Create ‘A’: 
x = randi(9, 5, 1);
y = randi(9, 5, 1);
A = x*pinv(y);
xc = A*y;               % Check

Answer 2

[Immelmann]

Thank you. It works and I will certainly make use of pinv function. But for my current special problem I look for a matrix A (as below) with coefficients "+-1" or "0" (which is always possible in my case). Is there a way to force matlab use only certain matrix entries?

 A  
 [1  0  1;...
  0  0 -1;...
  0  1  0]

[Star Strider]

My pleasure.

I never needed to do that, so I can only guess that the way to do it might be using a constrained optimisation routine (Optimization Toolbox) or perhaps using a genetic algorithm (Global Optimization Toolbox).

I would personally go for the genetic algorithm because I have more experience with them. They are also free of gradient descent constraints, and are free to roam your solution space to find appropriate results. You can constrain them if necessary as your requirements dictate. If you don’t have the Global Optimization Toolbox, unconstrained genetic algorithms are also easy to write. In this instance, your ‘population’ are ‘individuals’ (vectors) with trinary ‘states’ {-1,0,+1} that you can then form into matrices (use the reshape function) to test in your fitness function. Since you already know ‘x’ and ‘y’, your fitness function would be to minimise norm(x-A*y), with ‘A’ being each of your ‘individual’ or ‘chromosome’ vectors reshaped into an appropriate-sized matrix.