Identities of matrix powers of a matrix and matrix power of matrix on lie groups
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.
Review
World Journal of Advanced Engineering Technology and Sciences, 2024, 11(02), 624–627.
Article DOI: 10.30574/wjaets.2024.11.2.0150
Publication history:
Received on 17 March 2024; revised on 24 April 2024; accepted on 27 April 2024
Abstract:
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.
Keywords:
Matrix exponential; Matrix logarithm; Matrix powers of matrix; Matrix Lie group
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