利用微分求数量函数对矩阵变量的导数  

Finding the Derivative of a Quantitative Function with Respect to a Matrix Variable by Using Differentiation

作　　者：杨衍婷 YANG Yan-ting(School of Mathematics and Statistics,Xianyang Normal University,Xianyang Shaanxi,712000)

机构地区：[1]咸阳师范学院数学与统计学院,陕西咸阳712000

出　　处：《山西大同大学学报（自然科学版）》2022年第2期33-35,共3页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：咸阳师范学院青年骨干教师计划项目[XSYGG201801]。

摘　　要：在研究优化等问题时会遇到数量函数对矩阵变量的导数,总结了利用矩阵微分的性质以及微分和导数的关系求数量函数对矩阵变量的导数,给出具体的应用实例,从实例中可以看出,相比于按照矩阵导数的定义求导,利用微分求数量函数对矩阵变量的导数运算简单,可操作性强。When studying optimization and other problems, the derivative of a quantitative function to a matrix variable will occur. In this paper, using the properties of matrix differential and the relationship between differential and derivative to calculate the derivative of a quantitative function to a matrix variable is summarized and some specific application examples are given. From these examples, it can be seen that compared with finding the derivative according to the definition of matrix derivative, it is easy and maneuverable to calculate the derivative of a quantitative function to a matrix variable by differential method.

关 键 词：数量函数 矩阵值函数 导数 微分 

分 类 号：O151.21[理学—数学]