A Dynamic Matrix Exponential Via a Matrix Cylinder Transformation

Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Cylinder transformation; Matrix exponential; Time scales calculus

International Standard Serial Number (ISSN)

0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019Elsevier Inc., All rights reserved.

Publication Date

01 Nov 2019

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