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Topic: Question on Rudin's Principles of Mathematical Analysis 3rd edition
-- addressed to those who have access to book

Replies: 5   Last Post: Jun 3, 2013 5:53 PM

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David C. Ullrich

Posts: 2,752
Registered: 12/13/04
Re: Question on Rudin's Principles of Mathematical Analysis 3rd edition -- addressed to those who have access to book
Posted: Jun 3, 2013 1:06 PM
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On 2 Jun 2013 18:55:54 GMT, Bart Goddard <goddardbe@netscape.net>
wrote:

>dullrich@sprynet.com wrote in
>news:113nq812gfc5jgal5goutsdb190b6mg2r1@4ax.com:
>

>>>Sorry, I think I can answer my own question. The Jacobian (as defined
>>>by Rudin, anyway) means the determinant.

>>
>> As far as I know the Jacobian always means the determinant. Or the
>> absolute value of the determinant. Who defines it otherwise?
>> (In what seems to me to be very standard terminology, the
>> matrix in question is the _derivative_.)

>
>My prof, in 1980, stressed that the derivative was not the
>matrix, but the linear transformation which the matrix represents.


Well of course, that's what the derivative _really_ is. My
point was just that the matrix (or the linear transformation)
is definitely not the Jacobian.

As you suggest below, saying the matrix is the derivative
seems like a much better idea in low-level classes,
where abstraction is something one wants to avoid.
But among grownups yes, of course the derivative
is that linear transformation.

>We were using Spivak's Calculus on Manifolds, which I don't have
>near me at the moment, so I don't know if Spivak maintained the
>same distinction. (That prof was Jim Munkres.)
>
>I've never found the distinction valuable, so I don't make it
>when I teach vector calc stuff.
>
>B.





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