Solve system of matrices

Hello!

M1, M2 and M3, and C1, C2 and C3 are known 2x2 matrices

X and Y also 2x2, are unknown matrices to be determined from following set of equations

   M1=X*C1*Y. 
   M2=X*C2*Y. 
   M3=X*C3*Y.

How can we solve three systems to determine X?

Answer 1

[Christine Tobler]

I don't think this can be solved in general. The matrices X and Y contain 8 scalar unknowns together, but there are 12 scalar equations here (4 from each matrix equation). Do you have any additional knowledge about these systems?

You could take a look at gsvd and qz for some similar-looking decompositions, but I don't think they are what you are looking for.

Answer 2

[Aqeel Qureshi]

Thanks Christine!

This matrix representation is part of Network Analyzer calibration routine, brief details of which are mentioned in the attachment.

gsvd and qz doesn't seem to work this out.