Here were the systems used in the BBC matrix trials:
Matrix A was QS, no logic.
Matrix B was SQ, no logic.
Matrix C was QS, with logic.
Matrix D was SQ, with logic.
Matrix E was a tetrahedral matrix Peter Scheiber proposed for high separation.
Matrix F was UMX (BMX), no logic.
Matrix G was matrix F modified to reduce the phasey stereo image.
Matrix GX was G modified to reduce the phasey stereo image. (GX was not tested in the trials.)
Matrix HX was GX further modified to reduce the phasey stereo image. (HX was not tested in the trials.)
Matrix H was Matrix HX further modified to reduce phasiness.
Matrix J was H further modified to reduce phasiness. (This was done after the trials ended.)
Matrix HJ was J further modified to reduce phasiness. (This was done after the trials ended.)
Matrix HJ was later renamed UHJ.
When I read the BBC articles, I was surprised that neither EV matrix was tested. They have higher front-to-back separations and a higher left-front-to-right-front separations than any of the systems tested, ideal for classical music. I think they were wanting an all-channels-equal system, which neither EV system had.
I wonder if Matrix B was an SQ 10-40 decoder, or decoded the corner modulations without blending.
Note that Matrix A and Matrix C used the same QS recordings.
Matrix B and Matrix D used the same SQ recordings.