摘要
矩阵指数函数exp（A）、exp（At）在微分方程、现代系统与控制以及工程技术众多领域具有重要的应用。以矩阵指数函数各种导数的积分表现形式为基础,通过矩阵列展开运算的方法与技巧,获得了其一阶方向导数、梯度和一般矩阵导数的几个幂级数展开的理论计算公式,具有一定的理论和实际意义。
The matrix exponentials,exp（A） and exp（At）,play an important role in differential equation,modern systems and cybernetics,and engineering technique.In this paper,several computation formulae of power series expansion of matrix exponential derivatives are given.These proposed methods are achieved by matrix column expand operation based on the integral representation of various derivatives of matrix exponential.They have some significance of theory and practical application.
出处
《装备指挥技术学院学报》
2009年第6期111-113,共3页
Journal of the Academy of Equipment Command & Technology
关键词
矩阵指数函数
矩阵导数
矩阵幂级数
matrix exponentials
matrix derivatives
matrix power series
