A q-analogue of the matrix sixth Painlevé system

We derive a q-analogue of the matrix sixth Painlevé system from a connection-preserving deformation of a certain Fuchsian linear q-difference system. In specifying the linear q-difference system, we utilize the correspondence between linear differential systems and linear q-difference systems from the viewpoint of the spectral type. The system of non-linear q-difference equations thus obtained can also be regarded as a non-abelian analogue of Jimbo–Sakai's q–P _VI. (paper)