. In this paper, the q-derivative operator for matrix functions is defined, and q-calculus is examined in a broader context. The q-matrix exponential, the q-binomial of two matrices, and q-trigonometric and q-hyperbolic matrix functions are introduced. The q-derivatives of these newly defined functions are calculated in detail, and the fundamental properties of these structures are investigated. This study provides new insights into the interactions between q-calculus and matrix analysis.
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