Partial derivative of matrix functions with respect to a vector variable

The partial derivatives of scalar functions and vector functions with respect to a vector variable are defined and used in dynamics of multibody systems. However the partial derivative of matrix functions with respect to a vector variable is also still limited. In this paper firstly the definitions...

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Bibliographic Details
Main Author: Nguyen Van Khang
Format: Article
Language:English
Published: Publishing House for Science and Technology 2008-12-01
Series:Vietnam Journal of Mechanics
Online Access:https://vjs.ac.vn/index.php/vjmech/article/view/5632
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Summary:The partial derivatives of scalar functions and vector functions with respect to a vector variable are defined and used in dynamics of multibody systems. However the partial derivative of matrix functions with respect to a vector variable is also still limited. In this paper firstly the definitions of partial derivatives of scalar functions, vector functions and matrix functions with respect to a vector variable are represented systematically. After an overview of the matrix calculus related to Kronecker products is presented. Two theorems which specify the relationship between the time derivative of a matrix and its partial derivative with respect to a vector, and the partial derivative of product of two matrices with respect to a vector, are then proved.
ISSN:0866-7136
2815-5882