Partial derivative of matrix functions with respect to a vector variable

Nguyen Van Khang

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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DOI: https://doi.org/10.15625/0866-7136/30/4/5632 Display counter: Abstract : 38 views. PDF : 1187 views.

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