For a MIMO wireless communication system having $3$ Transmitter antennas and $4$ Receiver Antennas the channel matrix is: $412220\mathrm{.}329\mathrm{.}560\mathrm{.}10\mathrm{.}20\mathrm{.}40\mathrm{.}3210\mathrm{.}531\mathrm{.}80\mathrm{.}73$ j j j j j H j j j j j $+++=++$ Consider a set of $3$ symbols $[1,2,3]$ are to be sent. Consider both Transmitter and Receiver has channel distribution information. Let the noise received in the receiver antennas are of AWGN type and have the variances $[1,1\mathrm{.}5,2].$ a$)$ Find the eigenvalues of the channel matrix. b$)$ If there is a upper limit of the total transmit power of $3$dB$.$ What should be the power of the individual channel? c$)$ What should be the Channel Capacity?