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Suppose M is a 20 by 3 complex matrix, and I'd like to SVD. For example, in Matlab, I can do easily with:

[U, S, V] = svd(M);

where U, S, and V are complex matrices of20x20, 20x3, and 3x3, respectively.

However, I'd like to make U, a 20x20 matrix, to be either real matrix or near-real matrix (i.e., imaginary parts in the matrix are very small). S and V are okay with complex matrices. Having a real matrix is desirable for me in that it can minimize the overhead of computation in my program code.

I have no idea such approximation or decomposition exists. Is it possible?

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    If M is Symmetric(Hermitian) then I think U will be real. I'm pretty certain U can't be assured to be real in the general case, but I'm not sure about "near-real".2011-03-12
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    Thanks. M is not symmetric or Hermitian. S actually contains complex numbers. My question then would be there is any further transform or approximation...2011-03-12

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