Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124220230701Real powers and logarithms of matrices9510417266410.30504/jims.2023.385127.1088ENF.MirzapourDepartment of Mathematics, Faculty of science, University of Zanjan, Zanjan, Iran.0000-0001-7477-6475R.EskandariDepartment of Mathematics, Farhangian UniversityJournal Article20230208We define the logarithm function and the power function for matrices. Additionally, we investigate further properties of the logarithm and power functions. Utilizing the sign function, we propose a novel approach to representing the power function. Furthermore, we compute the power function for various types of matrices, including Hermitian, orthogonal, and symmetric matrices.https://jims.ims.ir/article_172664_f1ec15f62c2f405d451a0e4e4a585f95.pdf