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March 2nd, 2017, 01:01 AM  #1 
Newbie Joined: Oct 2016 From: Singapore Posts: 11 Thanks: 0  Help needed with partial differentiation equation of matrices
With reference to Eq. 16 in the attachment, I need help in understanding how the partial differentiation is done to obtain the answers in Eq. 17. Eqs. 10, 11, and 15 are the inputs needed to solve Eq. 16. I am puzzled how a matrix could be differentiated with respect to another matrix. I would highly appreciate it if an example calculation can be shown. Thanks in advance! 
March 2nd, 2017, 01:43 AM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,500 Thanks: 757 
They give you the formula to use $R_{i\_{st}} = \displaystyle{\sum_{k=1}^3}~R_k \dfrac{\partial v_k}{\partial v_{i \_{st}}}$ a bit of examination reveals that $\dfrac{\partial v_k}{\partial v_{i \_{st}}} = v_k \cdot v_{i \_ st}$ 
March 2nd, 2017, 04:09 AM  #3 
Newbie Joined: Oct 2016 From: Singapore Posts: 11 Thanks: 0 
Hi romsek, thanks for responding. I have some questions: 1) Which maths principle did you use to arrive at the dot product? 2) vk and vi_st are both 1x3 matrices. Isn't it not possible to perform the dot product? Thanks 
March 2nd, 2017, 09:30 AM  #4  
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,500 Thanks: 757  Quote:
2) think about your question  
March 3rd, 2017, 02:20 AM  #5 
Newbie Joined: Oct 2016 From: Singapore Posts: 11 Thanks: 0 
The dot product will work if vi_st is transposed to a 3x1 matrix. With this I can get the answers in Eq. 17


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differentiation, equation, matrices, needed, partial 
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