  We address the problem of interference leakage (IL) minimization in the
$K$-user multiple-input multiple-output (MIMO) interference channel (IC)
assisted by a reconfigurable intelligent surface (RIS). We describe an
iterative algorithm based on block coordinate descent to minimize the IL cost
function. A reformulation of the problem provides a geometric interpretation
and shows interesting connections with envelope precoding and phase-only
zero-forcing beamforming problems. As a result of this analysis, we derive a
set of necessary (but not sufficient) conditions for a phase-optimized RIS to
be able to perfectly cancel the interference on the $K$-user MIMO IC.
