Wavelength and polarization are two fundamental properties of light within which information can be encoded and (de)multiplexed. While wavelength-selective systems have widely proliferated, polarization-addressable active photonics has not seen notable progress, primarily because tunable and polarization-selective nanostructures have been elusive. Here, we introduce hybridized-active-dielectric (HAD) nanowires to achieve polarization-selective tunability. We then demonstrate the ability to use polarization as a parameter to selectively modulate the conductance of individual nanowires within a multi-nanowire system. By using polarization as the tunable vector, we show matrix-vector multiplication in a nanowire device configuration. While our HAD nanowires use phase-change materials as the active material, this concept is readily generalized to other active materials hybridized with dielectrics and thus has the potential in a broad range of applications from photonic memories and routing to polarization-multiplexed computing.