My Math Forum Help needed with partial differentiation equation of matrices

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March 2nd, 2017, 01:01 AM   #1
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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!
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 March 2nd, 2017, 01:43 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 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
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Quote:
 Originally Posted by mikeraj 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
1) i used the ancient method of looking at the results and the formula used to get them to identify the unknown piece.

 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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