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-   -   prove jacobian matrix is identity of matrix of order 3 (http://www.physicsforums.com/showthread.php?t=348830)

 CrimsnDragn Oct25-09 03:36 PM

prove jacobian matrix is identity of matrix of order 3

If f(x,y,z) = xi + yj +zk, prove that Jacobian matrix Df(x,y,z) is the identity matrix of order 3.

Because the D operator is linear, D1f(x,y,z) = i, D2f(x,y,z) = k, D3f(x,y,z) = k

There is clearly a relationship between this and some sort of identity, but I'm not sure how to state it, and I don't understand the order of linear transformations. Could someone help me?

 CrimsnDragn Oct25-09 03:42 PM

Re: prove jacobian matrix is identity of matrix of order 3

*typo on D2f(x,y,z) = j

actually I was just rethinking about the problem. could Df(x,y,z) = ((1,0,0),(0,1,0),(0,0,1)), which becomes an identity matrix, and the order of 3 refers to 3x3 matrix?

 Dick Oct25-09 04:01 PM

Re: prove jacobian matrix is identity of matrix of order 3

Quote:
 Quote by CrimsnDragn (Post 2410140) *typo on D2f(x,y,z) = j actually I was just rethinking about the problem. could Df(x,y,z) = ((1,0,0),(0,1,0),(0,0,1)), which becomes an identity matrix, and the order of 3 refers to 3x3 matrix?
Yes, exactly.

 CrimsnDragn Oct25-09 08:10 PM

Re: prove jacobian matrix is identity of matrix of order 3

awesome. thanks!

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