  This letter investigates the joint active and passive beamforming
optimization for intelligent reflecting surface (IRS) aided multiuser
multiple-input multiple-output systems with the objective of maximizing the
weighted sum-rate. We show that this problem can be solved via a matrix
weighted mean square error minimization equivalence. In particular, for the
optimization of the passive IRS beamforming, we first propose an iterative
algorithm with excellent performance based on the manifold optimization. By
using the matrix fractional programming technique to obtain a more tractable
object function, we then propose a low complexity algorithm based on the
majorization-minimization method. Numerical results verify the convergence of
our proposed algorithms and the significant performance improvement over the
communication scenario without IRS assistance.
