Defining a matrix, $\displaystyle \mathbf{X}$

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

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

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

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

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

Thanks.