  This paper introduces a fast algorithm for simultaneous inversion and
determinant computation of small sized matrices in the context of fully
Polarimetric Synthetic Aperture Radar (PolSAR) image processing and analysis.
The proposed fast algorithm is based on the computation of the adjoint matrix
and the symmetry of the input matrix. The algorithm is implemented in a general
purpose graphical processing unit (GPGPU) and compared to the usual approach
based on Cholesky factorization. The assessment with simulated observations and
data from an actual PolSAR sensor show a speedup factor of about two when
compared to the usual Cholesky factorization. Moreover, the expressions
provided here can be implemented in any platform.
