My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 2nd, 2017, 02:01 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!
Attached Images
File Type: jpg Equations.JPG (32.1 KB, 2 views)
mikeraj is offline  
 
March 2nd, 2017, 02:43 AM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,237
Thanks: 637

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

$\dfrac{\partial v_k}{\partial v_{i \_{st}}} = v_k \cdot v_{i \_ st}$
romsek is offline  
March 2nd, 2017, 05:09 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
mikeraj is offline  
March 2nd, 2017, 10:30 AM   #4
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,237
Thanks: 637

Quote:
Originally Posted by mikeraj View Post
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.

2) think about your question
romsek is offline  
March 3rd, 2017, 03:20 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
mikeraj is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
differentiation, equation, matrices, needed, partial



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help needed with partial differentiation equation of matrices mikeraj Linear Algebra 3 March 5th, 2017 05:17 AM
Help Needed With Partial Fraction Decomposition mathdisciple Calculus 2 March 23rd, 2014 11:49 PM
Urgent help needed for differentiation asifrahman1988 Calculus 2 October 27th, 2012 04:06 PM
partial differentiation please help vtek Calculus 1 February 19th, 2012 10:16 AM
Partial Differentiation...help jakeward Calculus 3 December 13th, 2010 04:39 PM





Copyright © 2017 My Math Forum. All rights reserved.