How to solve Sylvester Equations?

All are 2*2 matrices with complex values.

P1 and P2: known with small errors (experimental errors)

Q1 and Q2: known with small errors (experimental errors)

X and Y: unknown

X*P1*Y = Q1

X*P2*Y = Q2

How to solve X and Y as the best fist of the equations above?

Thanks in advance!

Answer 1

[Walter Roberson]

Possibly this previous discussion might help.

[Ellen]

Thanks!

His equation is in the form of A*X+B*X=C, while I am trying to solve X and Y with two equations.

[Dr. Seis]

So... solve for "X" or solve for "Y" in one equation and then plug the result into the second equation - you will find that you have an equation of the correct form to use the "lyap" function.

[Ellen]

Yes, if I solve "X" or "Y" in one equation and plug into the second equation - I get in the form of A*X=X*B. This equation does not have a unique solution in many cases.

My question is if it is possible to get a unique solution of X and Y from two equations.

Thanks all.