### Partial derivative of matrix functions with respect to a vector variable

#### 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.

#### Full Text:

PDFDOI: https://doi.org/10.15625/0866-7136/30/4/5632 Display counter: Abstract : 50 views. PDF : 1320 views.

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