System and method for dimension reduction and for channel and interference condition feedback in a Multi-User Multiple-Input-Multiple-Output (MU MIMO) wireless communication systems are provided herein. The method for dimension reduction includes determining a number of virtual antennas, vk, for beamformees pertaining to a multi user (MU) transmission group, reducing the dimension of the matrix by selecting a sub-set of antennas or by Eigen mode selection and sending a reduced dimension candidate transmit beamforming matrix or an effective channel matrix to a beamformer. The method for channel and interference condition feedback Interference condition includes sending to a beamformee metric indicative of the interference level from other streams.