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 |
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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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| _version_ | 1850044451307651072 |
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| author | Nguyen Van Khang |
| author_facet | Nguyen Van Khang |
| author_sort | Nguyen Van Khang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2e7308d45c7d417da815dc454284d276 |
| institution | DOAJ |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2008-12-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-2e7308d45c7d417da815dc454284d2762025-08-20T02:54:58ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822008-12-0130410.15625/0866-7136/30/4/5632Partial derivative of matrix functions with respect to a vector variableNguyen Van Khang0Hanoi University of Technology, VietnamThe 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.https://vjs.ac.vn/index.php/vjmech/article/view/5632 |
| spellingShingle | Nguyen Van Khang Partial derivative of matrix functions with respect to a vector variable Vietnam Journal of Mechanics |
| title | Partial derivative of matrix functions with respect to a vector variable |
| title_full | Partial derivative of matrix functions with respect to a vector variable |
| title_fullStr | Partial derivative of matrix functions with respect to a vector variable |
| title_full_unstemmed | Partial derivative of matrix functions with respect to a vector variable |
| title_short | Partial derivative of matrix functions with respect to a vector variable |
| title_sort | partial derivative of matrix functions with respect to a vector variable |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/5632 |
| work_keys_str_mv | AT nguyenvankhang partialderivativeofmatrixfunctionswithrespecttoavectorvariable |