gaffar
Member level 1
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 \[tr(.)\] is trace operator, \[c\] is a constant, and \[\mathbf{X}^H\] is the Hermitian (complex transpose) of \[\mathbf{X}\].
Thanks.
\[\mathbf{X}=(\mathbf{A}+\mu \mathbf{I})^{-1}\mathbf{B}\]
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 \[tr(.)\] is trace operator, \[c\] is a constant, and \[\mathbf{X}^H\] is the Hermitian (complex transpose) of \[\mathbf{X}\].
Thanks.
