A dynamic matrix exponential via a matrix cylinder transformation
Journal of Mathematical Analysis and Applications
In this work, we develop a new matrix exponential on time scales via a cylinder transformation with a component-wise, locally μΔ-integrable square matrix subscript. Our resulting matrix function can be written in terms of the matrix exponential of a Lebesgue integral added to a logarithmic sum in terms of the gaps of a general time scale. Under strict commutativity conditions, we show our dynamic matrix exponential is equivalent to the one in the standard literature. Finally, we demonstrate that our matrix exponential satisfies a nonlinear dynamic integral equation.
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Cuchta, Tom; Grow, David; and Wintz, Nick, "A dynamic matrix exponential via a matrix cylinder transformation" (2019). Faculty Scholarship. 21.