Centralized algorithms for weighted sum rate (WSR) maximization for the K-user frequency-flat MIMO Interference Channel (MIMO IFC) with full channel state information (CSI) are considered. Maximization of WSR is desirable since it allows the system to cover all the rate tuples on the rate region boundary for a given MIMO IFC. First, we propose an iterative algorithm to design optimal linear transmitters and receivers. The transmitters and receivers are optimized to maximize the WSR of the MIMO IFC. Subsequently, we propose a greedy user selection algorithm based on the maximum WSR algorithm that can be applied to select a subset of transmit-receive pairs that cooperate in the interest of maximizing the sum-rate of the resulting cooperative network. To the best of our knowledge this is the first time user selection has been proposed in the context of the MIMO IFC.