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In this study, linear second-order matrix q-difference equations are shown to be formally self-adjoint equations with respect to a certain inner prod- uct and the associated self-adjoint boundary conditions. A generalized Wronskian is introduced and a Lagrange identity and Abel's formula are established. Two reduction-of-order theorems are given. The analysis and characterization of q- dominant and q-recessive solutions at infinity are presented, emphasizing the case when the quantum system is disconjugate.

q-Dominant and q-recessive matrix solutions for linear quantum systems