I have a question regarding how to calculate unknown vector from sdp matrix.
I have a known vector of X=[X1 X2 X3], where X1, X2 and X3 are complex numbers and known, and I also have a vector of Y=[Y1 Y2 Y3].
I defined my sdp matrix of W = X*Y’, my question is how can i get Y vector variables using W matrix?

Can you please state more clearly what is known, i.e., what are the inputs and constraints, and what is to be found? Do you have a well-thought through mathematical problem?

Note that if X and Y are column vectors, then X*Y' is a rank one matrix, i.e., all but one eigenvalues = 0.

Yes, rank(W) should be 1, but I do not use it under constraints; my only constraint on W is W >= 0.
Actually what I’m trying to do is explained as following:

Please provide a self-contained and complete mathematical description of the problem, with a consistent notation. Exactly what the inputs are, what is known, what the constraints are, and what is unknown.

As currently written, mind-reading ability seems to be needed more so than optimization or linear algebra knowledge in order to solve your problem, whatever it is.

Mark’s actually being more patient that I am (thank you Mark!)

This forum is not for general modeling assistance, it is for assistance on actual CVX usage. You’ve presented no code here so there’s no indication that you’ve begun the CVX modeling process. If you haven’t, please consult the users guide, example library, etc. for assistance.

But more importantly, by showing us the model you do have, and asking for help with specific pieces of it, you’re more likely to communicate to us effectively exactly what help you need.

That construct was designed to achieve V0*V1' and V1*V0’ to be rank one. There is nothing forcing W1 to be rank one. In this example, though it comes out to the zeros matrix (within tolerance).

Yes. I know that, but the system that I’m working on well known one and reported as it gives rank 1 solution. My question was that I’m wondering if there is something obvious that I’m missing.