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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!
Attached Images Equations.JPG (32.1 KB, 2 views) March 2nd, 2017, 01:43 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 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 Tags differentiation, equation, matrices, needed, partial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mikeraj Linear Algebra 3 March 5th, 2017 04:17 AM mathdisciple Calculus 2 March 23rd, 2014 11:49 PM asifrahman1988 Calculus 2 October 27th, 2012 04:06 PM vtek Calculus 1 February 19th, 2012 09:16 AM jakeward Calculus 3 December 13th, 2010 03:39 PM

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