Abstract
In this paper, we prove that the solution of the autonomousq-difference systemDqYx=AYqxwith the initial conditionY0=Y0whereAis a constant square complex matrix,Dqis the Jacksonq-derivative and0<q<1, is asymptotically stable if and only ifℜλ<0for allλ∈σAwhereσAis the set of all eigenvalues ofA(the spectrum ofA). This results are exploited to provide the orthogonality property of the discreteq-Hermite matrix polynomials.
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