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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| Format: | Article |
| Language: | English |
| Published: |
Publishing House for Science and Technology
2008-12-01
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| 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. |
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| ISSN: | 0866-7136 2815-5882 |