TY - JOUR AU - Khang, Nguyen Van PY - 2008/12/31 Y2 - 2024/03/29 TI - Partial derivative of matrix functions with respect to a vector variable JF - Vietnam Journal of Mechanics JA - Vietnam J. Mech. VL - 30 IS - 4 SE - Research Article DO - 10.15625/0866-7136/30/4/5632 UR - https://vjs.ac.vn/index.php/vjmech/article/view/5632 SP - 269 – 279 AB - 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. ER -