1 Department of Mathematics, Faculty of Applied Sciences, University of Sri Jayewardenepura, Gangodawilla, Nugegoda 10250. Sri Lanka.
2 Department of Mathematics and Philosophy of Engineering, Faculty of Engineering Technology, The Open University of Sri Lanka, Nawala, Nugegoda, 10250. Sri Lanka.
Received on 17 March 2024; revised on 24 April 2024; accepted on 27 April 2024
This paper introduces fundamental definitions pertaining to Matrix Lie Groups and Lie Algebra. We illustrate the concepts of the exponential of a matrix and the logarithm of a matrix as integral components of our discourse. We introduce novel identities related to the matrix powers of a matrix. To prove these identities, we employ the results of the matrix powers of a matrix. Finally, we derive an expression for the matrix powers of a matrix within the context of a connected matrix lie group.
Matrix exponential; Matrix logarithm; Matrix powers of matrix; Matrix Lie group
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K. K. W. A. S. Kumara and G. Nandasena. Identities of matrix powers of a matrix and matrix power of matrix on lie groups. World Journal of Advanced Engineering Technology and Sciences, 2024, 11(02), 624–627. Article DOI: https://doi.org/10.30574/wjaets.2024.11.2.0150