论文标题
一些针对矩阵指数的明确公式，矩阵对数，矩阵的$ n $ th功率及其drazin倒置
Some Explicit Formulas for Matrix Exponential, Matrix Logarithm, the $n$th Power of Matrices and their Drazin Inverses
论文作者
论文摘要
在这项工作中，提供了针对矩阵指数的新闭合公式。我们的方法是直接和基本的，它提供了有关此基本主题的广泛文献中可进行的可管理公式。此外，其他人被恢复和普遍。结果，我们很容易获得chevalley {Jordan分解和任何矩阵的光谱投影。此外，提出了矩阵及其drazin倒置的任意积极能力的封闭形式表达式。使用这些结果，获得了用于矩阵对数的优雅显式公式。制定了几种特殊情况和示例，以说明本文介绍的方法。
In this work, new closed-form formulas for the matrix exponential are provided. Our method is direct and elementary, it gives tractable and manageable formulas not current in the extensive literature on this essential subject. Moreover, others are recuperated and generalized. As a consequence, we easily obtain the Chevalley{Jordan decomposition and the spectral projections of any matrix. In addition, closed-form expressions for the arbitrary positive powers of matrices and their Drazin inverses are presented. Using these results, an elegant explicit formula for logarithm of matrices is obtained. Several particular cases and examples are formulated to illustrate the methods presented in this paper.
