  For multiple-input/multiple-output (MIMO) spatial multiplexing with
zero-forcing detection (ZF), signal-to-noise ratio (SNR) analysis for Rician
fading involves the cumbersome noncentral-Wishart distribution (NCWD) of the
transmit sample-correlation (Gramian) matrix. An \textsl{approximation} with a
\textsl{virtual} CWD previously yielded for the ZF SNR an approximate (virtual)
Gamma distribution. However, analytical conditions qualifying the accuracy of
the SNR-distribution approximation were unknown. Therefore, we have been
attempting to exactly characterize ZF SNR for Rician fading. Our previous
attempts succeeded only for the sole Rician-fading stream under
Rician--Rayleigh fading, by writing it as scalar Schur complement (SC) in the
Gramian. Herein, we pursue a more general, matrix-SC-based analysis to
characterize SNRs when several streams may undergo Rician fading. On one hand,
for full-Rician fading, the SC distribution is found to be exactly a CWD if and
only if a channel-mean--correlation \textsl{condition} holds. Interestingly,
this CWD then coincides with the \textsl{virtual} CWD ensuing from the
\textsl{approximation}. Thus, under the \textsl{condition}, the actual and
virtual SNR-distributions coincide. On the other hand, for Rician--Rayleigh
fading, the matrix-SC distribution is characterized in terms of determinant of
matrix with elementary-function entries, which also yields a new
characterization of the ZF SNR. Average error probability results validate our
analysis vs.~simulation.
