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I have a problem with the following matrix equation:

A = B*inv(B+D)

where A is a square matrix, B a positive semi-definite matrix, D a positive diagonal matrix and inv() denotes the inverse matrix. All are real-valued.

Does anyone know of any simple way to check whether this equation has a solution for given A? And how to obtain this solution? (i.e. find B and D) And whether the solution is unique?

Thanks in advance!

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# Matrix decomposition question

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