In case you are working with Sentinel-1 data, C2 and T2 matrix operators will not give you good results in a polarimetric sense, because they actually combine HH and VV. These are not available for S1 products, only VV/VH or HH/HV.
The concept of dual-polarization to describe scattering mechanisms is not really applicable here, yet SNAP allows to compute them.
This is nicely demonstrated in this article: Remote Sensing | Free Full-Text | Scattering Mechanism Extraction by a Modified Cloude-Pottier Decomposition for Dual Polarization SAR
Thus, HH-VV SAR is a suitable alternative to full-polarization SAR in certain cases. Meanwhile, the extraction performance of the other two dual-polarization SARs is badly degraded due to the lack of co-polarization. Therefore, HH-HV and HV-VV SARs cannot effectively extract the scattering mechanisms in the H-α plane.
And another explanation: Covariance Matrix C2 for Sentinel-1 --Diagonal Elements