Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 4 2 2023 07 01 Real powers and logarithms of matrices 95 104 172664 10.30504/jims.2023.385127.1088 EN F. Mirzapour Department of Mathematics, Faculty of science, University of Zanjan, Zanjan, Iran. 0000-0001-7477-6475 R. Eskandari Department of Mathematics, Farhangian University Journal Article 2023 02 08 We 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. Matrix Power logarithm https://jims.ims.ir/article_172664_f2974fd047890253ff7b27c498a3ae55.pdf