Defining a matrix, \mathbf{X}

\mathbf{X}=(\mathbf{A}+\mu \mathbf{I})^{-1}\mathbf{B}

where \mathbf{B} is a N\times M matrix, \mathbf{A} is a N\times N matrix, \mu is a scalar, and \mathbf{I} is a N\times N identity matrix.

We would like to find \mu, satisfying the following equation:

tr(\mathbf{XX}^H)=c

where tr(.) shows trace operator, c is a constant, and \mathbf{X}^H is the Hermitian (complex transpose) of \mathbf{X}.

Thanks.