期刊
OPEN MATHEMATICS
卷 19, 期 1, 页码 1771-1778出版社
DE GRUYTER POLAND SP Z O O
DOI: 10.1515/math-2021-0135
关键词
derivative of matrix functions; Cauchy integral formula; matrix function; Hamilton-Cayley theorem; analytic function
类别
资金
- Science and Technology Project of Jiangxi Provincial Department of Education [GJJ180944, GJJ190963]
- Chongqing Natural Science Foundation Project [cstc2019jcyj-msxmX0390]
A new type of derivative of matrix functions is defined in this paper, and it is proven that the higher-order derivative form of the Cauchy integral formula for matrix functions holds under this new definition. Additionally, examples of calculating matrix function values using the Cauchy integral formula and its higher-order derivative form are provided.
The derivative of a n-order matrix function on the complex field is usually defined as a n(2)-order matrix, which is not suitable for generalizing Cauchy integral formula of matrix functions to its higher-order derivative form. In this paper, a new kind of derivative of matrix functions is defined, and the higher-order derivative form of Cauchy integral formula of matrix functions is also proved to be true under the new kind of definition of derivative. At the same time, some examples about calculating the values of matrix functions by using Cauchy integral formula of matrix functions and its higher-order derivative formare given.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据