Partial derivative of matrix functions with respect to a vector variable

Authors

  • Nguyen Van Khang Hanoi University of Technology, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/30/4/5632

Abstract

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.

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Published

31-12-2008

How to Cite

Khang, N. V. (2008). Partial derivative of matrix functions with respect to a vector variable. Vietnam Journal of Mechanics, 30(4), 269 –. https://doi.org/10.15625/0866-7136/30/4/5632

Issue

Section

Research Paper

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