  In general relativity, gravitational waves (GWs) exhibit two tensor modes,
while alternative theories predict up to six polarization modes. We investigate
GW polarization constraints using a model-independent parametrized
post-Einsteinian framework with space- and ground-based detectors. Evaluating
LISA, Taiji, TianQin, LIGO, Virgo, KAGRA, and Einstein Telescope (ET), we
analyze their capabilities and network performance. Taiji provides the best
constraints among space-based detectors, with LISA outperforming TianQin. Among
ground-based detectors, LIGO excels in vector modes, while ET offers the most
comprehensive constraints. In network scenarios, LISA+TJm performs best, and ET
surpasses second-generation detector combinations. Multiband observations
alleviate scalar mode degeneracies, significantly enhancing ground-based
detector performance. Combined space- and ground-based observations yield
robust constraints on GW polarization, advancing tests of deviations from
general relativity. Our findings highlight the potential of future GW missions
to refine our understanding of gravitational physics through precise
polarization measurements.
